First of all I should mention that the Chansey family are my most disliked mons so my post might be a little biased. I don't just hate Chansey, I absolutely loathe it and its evolution with an autistic rage only a neckbeard who has been playing this game competitively for 12 years can muster. I honest to god believe this thing is the biggest mistake Gamefreak has made in terms of game design. Even worse than evasion, even worse than mega Gengar/Mence/Kang/Rayquaza, even worse than Shadow Tag and even worse than Talonflame whose sole existence denied three entire types and speed boosters in general the possibility to sweep.
She's a blanket check to all special attackers, with in built counters to status induction, and on top of that functions amazingly as both a cleric with Wish and Heal Bell and as a status inducer with Toxic and Thunder Wave, on top of that she can deal a solid 50 damage to ANYTHING no matter their defenses with Seismic Toss or bait weaker physical attackers that might not KO her with Counter and remove them from the game.
I've been on and off Pokemmo for the past few months, I recently came back and noticed one thing, if they were on a favorable matchup that'd normally force a switch every special sweeper that could Trick would Trick their choice item into whatever switched into them. Be it Starmie, Alakazam, Slowbro or Espeon, the first thing they would do was Trick their choice item and pray that the opponent switched into Chansey. That speaks volumes of how influential Chansey is, her 50% usage means that these Trick leaps of faith are incredibly likely to work. This could be argued as a skillful play by the Trick users, they predict their opponent to switch into their Chansey and nail her, surely this will cripple her, they stopped the tumor from sitting on their special sweepers forever while supporting the rest of her team, now they can switch out and play the rest of the game! However I, as a person who refuses to use Canceregg and instead use Umbreon this is simply a free kill with Pursuit and even if the trickster survives, due to how common this leap of faith is I've opted for use Macho Brace on my Umbreon so their trickster now is either dead, or so slow my Blaziken and Venusaur don't have to worry if they switch into them.
Sadly even after tricking the choice item, this doesn't stop Chansey from being an incredibly useful pivot against most special attackers. Toxic and Thunder Wave remove any boosting Espeons, Slowbros and Alakazams as well as other walls/bulky pokemon that aren't fortunate enough to have Heal Bell or Rest, Thunder Wave heavily limits Venusaur and speedier pokemon that might break through her, Seismic Toss is still solid damage against anything switching in without recovery and she can still perform clerical duties with Heal Bell, so even if the leap of faith or "outplay" depending on your point of view pays off, she's not effectively useless because of it. I should also mention that while she's limited to one move, she takes so little damage from special moves that switching a few times into them and using one of those switches to heal up is perfectly viable even if it's technically a big momentum sink.
So basically:
Teambuilding is heavily limited to special attackers that either provide enough utility to support the rest of the team or special attackers that can trick their choice item on the switch, basically "all out attackers" are really rare unlike in the case of physical attackers.
Due to Chansey's status as a blanket check, aka something that generally walls every special attacker, it's fairly easy to pair her up with Pokemon that cover her obvious weaknesses and form. Skarmbliss (Which should be renamed Skarmsey due to Eviolite in later gens and the current mmo meta) is a core used from gen 2 to this day in gen 7 due to how effective it is, in a game with so much power creep that's insane. Pokemon like Weezing and Dusclops also provide amazing walling potential and are easy to fit into any team, so to have a great defensive core you just need Chansey to cover all your special attacking needs and then one or two Pokemon that can protect from 90% of physical attackers.
This also puts a lot of pressure on physical attackers as they'd need to run something to hit these walls hard enough on the switch until they are gone from the game and they can target Chansey, meanwhile no special attacker can deal enough damage to Chansey to the point where they can take it down and eventually put the opposing physical walls down. Essentially what I mean is the moment you remove the opponent's physical attackers, if you have a Chansey you automatically win unless you're dealing with Venusaur, on the other side Physical attackers can eventually break through Weezing/Skarmory/Dusclops/Arcanine.
The alternative for teambuilding is to run a hybrid attacker that can lure these physical walls by hitting them with special attacks and then eventually nail the Chansey.
It doesn't help that she's cheap as fuck to breed requiring only 3 IVs and a nature.
Inhibit, it's way too easy to fit into any team, it's versatile enough that you don't know what to switch into it without being crippled in one way or another. Bulky enough to cover an entire attacking type, bulky enough to not worry about walls attacking it (or statusing it), bulky enough to not worry about minor physical attackers attacking it and bulky enough to use Counter on physical attackers that don't one shot it for an effective trade or what could possibly be a win condition. Forces special attackers to do leaps of faith to remove her and stuff like Trapinch sees usage simply because it can remove her (Assuming she isn't one step ahead of the curv and runs Shed Shell).
If "skillful plays" imply "Oh! I switched my physical attacker in without getting crippled by status and then boosted!" or "I tricc her" then yes she encourages skillful play, but she also encourages everyone running bulky balance teams with her in the middle 50% of the time and encourages people to just spam physical attacks until the opposing physical walls are beaten into a bloody pulp.
Won't happen. As a person who doesn't use Chansey at all I have never seen this happen, special attackers have more checks than just Chansey and they don't need to have as much role compression as her.
Don't like being paralyzed and can usually be walled by stuff accompanying Chansey
I can deal with Chansey just fine, the same way I was able to deal with Snorlax just fine and the same way I'd be able to deal with any Uber (except Mence, that thing would plow me) easily if I had to bother.
Well bud, those are your team building skills being put to the test, you ought a be skillful enough to build a team that doesn't get plowed by newcomer mons, unless you're admitting to being unskillful enough to use Chansey as a crutch to get past most things.
Well at the end of the day after venting this much I'd like to ask, WHEN THE FUCK ARE WE GETTING AN UBERS QUEUE SO WE CAN STOP TREATING GETTING BANNED TO UBERS LIKE BEING SENT TO THE SHADOW REALM? A LOT OF PEOPLE WANNA USE THESE MONS DAMMIT.
Finally my belief regarding ban or no ban is don't ban her, lol machop used mega punch, dead egg much?? i just boost on her and win, nooblords, literally nothing that's currently UU would rise to OU if she's gone anyways you'd just see more eruption typlosion spam and maybe more offensive starmies