Partitioning in Game Design just involves limiting the number of elements that are accessible at any given time using criteria that can vary pretty wildly from factions and sub-factions to formats.
To use a simple example, in the original Mass Effect, there were 6 classes and their playstyles were pretty different despite a lot of overlap in terms of of available powers because each class only had limited access to powers combined with only being able to use certain armor and weapons. If you wanted to run head first at the enemy invincibly with guns blazing, go Soldier. If you wanted to make enemies into helpless floating piniatas or throw them across the room with your mind, go Adept. If you wanted to cower in a corner trying and failing to not die before going back to the character select screen to pick a different class, then go Engineer. As the series went on, though, the elements started to merge a lot with armor classes going away, weapons options opening up a lot more and culminating in the system in Mass Effect Andromeda. In Andromeda, you could basically take whatever abilities you wanted. Some of them required X points spent in Biotic, Tech or Combat trees, but that was about it. In turn, the series went from about 6ish playstyles (depending on whether or not you actually count the Engineer) to only about really 2, maybe 3.
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This brings us to heart of why so many games partition their elements. When confronted with everything, you'll see a few interesting dark horse options, but generally most players will just gravitate towards a handful of demonstrably correct answers. This can happen even when all the elements seem, on the surface to be perfectly balanced. For example, if I had a spell in Warmachine that added +2 to all ranged damage and another spell that added +2 to all melee damage, you would think these spells would be equal in game impact, but that's completely false. Mathematically, sure a unit gets the same benefit from 1 as the other, but a lot of considerations such as what other elements are available, whether other game mechanics or the meta favors one attack type over the other or what other spells are available to the caster, will wildly change the value of the spell. Despite providing an identical effect, these 2 spells will never be truly equal. In short, there will always be elements or combination of elements that are "more correct" i.e. that simply offer more of an edge in terms of efficiency or application over it's contemporaries. In this regards, if you give players access to every possible option, only a handful will see real play, in other words, the addition of more elements reduces available playstyles/archetypes. This works both for elements in direct competition with these more efficient options for list choices as well as those that have to compete against them from across the table.
For these reasons, most games have opted for a sort of artificial partitioning of their elements. Magic was one of the earliest and biggest when they moved heavily to the what was called "Type 2" at the time, but that more recent players will call Standard today. Hearthstone made a similar move. Warmachine/Hordes has gone heavily into theme lists that, while not specifically banning certain combinations, it does make out of theme lists far less desirable as they'll generally be at about 15-20% disadvantage between free models and theme benefits (which means any combo you're going out of theme for has to be really compelling). The most recent addition to this list is X-Wing with the announced split between Extended (play everything) and Hyperspace (only certain ships/upgrades allowed).
To put it simply, Partitioning your game becomes almost necessary once you're past a certain point. From the player perspective, unless some truly incredible releases hit, any game that has been going on long enough without major partitioning will generally devolve into a handful of set archetypes and the only question players will bother asking upon new releases is "does this impact an existing archetype? If so, how?" and anything that doesn't fit into the archetype or that doesn't offer a compelling advantage over an element already in an archetype gets discarded. You'll definitely see some elements that are defining enough to create their own archetypes, but those are far and away in the minority. As far as the players are concerned, the meta is relatively static. It will be solved and then resolved fairly quickly after any new release because the other elements that any new piece has to be compared to is already a known quantity. This also presents a troubling conundrum for a design team. How do you introduce more elements that are useful enough to see play, but not so powerful as to remove existing options? It's easy to answer that question early in a game's history, but as time goes on, it's becomes an almost insurmountable challenge that only allows 2 solutions 1: A static meta that people will get quickly bored with or 2: Introducing power creep that will outright negate old elements.
To try and contextualize this further, let's say Privateer Press didn't move heavily into themes for Warmachine/Hordes and wanted to introduce a new melee unit right now for Retribution of Scyrah, a roughly mid-sized faction. That new melee unit would have to be a viable option compared against, but not replacing, all of these units:
Mage Hunter Infiltrators Houseguard Halberdiers Dawnguard Sentinels Ryssovass Defenders House Ellowuyr Swordsmen
Releasing a new unit under that criteria would be really difficult and the most likely result is that it either becomes a dust collector or replaces 1 or more of them. Now let's introduce a new melee unit in a Theme heavy game. It's going to go into the Legion's of Dawn Theme, what does it have to compete with? Well, just the Dawnguard Sentinels whose role is pretty clear as armored and hard-hitting. That's a much easier task to undertake and you have a higher likelihood of just creating a viable options without replacing an existing one.
In terms of players, a meta with more partitioning means that each element within a given partition is far more impactful and more important. This creates far more dynamicism in terms of list building and variety and also creates a clearer distinction as to what each partition's role is and what's it's well suited for. For an example, Introducing a new ship into X-Wing likely won't do a whole lot in the extended format unless it's just better than other options. On the other side of the equation, Hyperspace only has a handful of ships per faction, so adding ships is pretty significant. It has a much higher potential to shake up current archetypes or create new ones. Additionally, because of the narrow partitioning in Hyperspace, even options that are not exactly optimal (things like U-Wings and TIE Strikers) have a much higher chance of seeing meaningful play than they ever would in Extended.
That being said, why do players frequently push back against partitioning? Well, definitely not all players do, but it's rare to see a game make a much narrower format without seeing at least some dissatisfaction. Part of it is the "I can't use my entire collection of cards/miniatures/ships" argument, but in truth, you couldn't use all of them anyways both in terms of list/deckbuilding restrictions and the fact that without the partition, many of those elements are just too inefficient to bother with. There isn't a meaningful difference between a game explicitly saying you can't use something and that element being so ineffectual into the meta that the game might as well be saying you can't use it. If you are worried about competitive play, they're basically the same, if you're not, who cares, play whatever format you want. Another part of it is the flawed argument that you're losing options. All you have to look at here is games like Magic and how many cards that would be an absolute waste of time in legacy see consistent play in standard. All of these "non-options" get to actually see time just because of the partition between game modes.
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What I find interesting, is that most players, even the ones against partitioning, have already accepted it's necessity. What would X-Wing look like if there were no faction restrictions on anything, ship or upgrade? What would magic look like if the color system was done away with and everything costed colorless mana? What would Hearthstone look like without class restrictions? What would Warmachine/Hordes look like if you could literally take any combination of models? Players have broadly already accepted that partitioning in the form of factions/mana colors/classes is not only necessary, but outright healthy for the game as a whole, so is it that hard to believe that as the game has progressed and new elements constantly added that further partitioning may be necessary to keep the game as a dynamic and engaging experience?