Well, your not doing anything to the player

. But it's not removing the character from the game, just effecting them. An archer with no bow can still go on the adventure.
This is disingenuous. I was referring to this:
I'm talking about when the character becomes a duck for several game sessions, maybe weeks or months in real life time.
I quoted that line and a few others. Turning a character into a duck for months radically diminishes and potentially entirely removes a player's ability to meaningfully play the game in a way that taking away a character's weapon, even their main weapon, does not. Honestly, I have trouble seeing the former as anything other than petty cruelty to inflict that sort of treatment on someone who I'm playing with.
As pointed out above, I never said "this never ever happens" or anything like that. I said it was rare in a Neo T game, yes. Any individual game can have bits and parts of others.
And here you're misrepresenting yourself. Let me quote you, once again:
But I would think only traditional has the events like the characters falling off a bridge into a raging river and loosing many of their items.
I've gone ahead and boldly the part where you say it's a feature of
only traditional play.
Also I note your only talking about taking the characters gear away for a short time, and then saying they will get it all back
Again, completely mischaracterizing what I explicitly said. They've already been without for several real-life weeks and will continue to be without for at least a couple more. That's precisely the thing that you said was characteristic of only traditional play!
Also, also, you don't mention what the gear is...is it just like "a pair of sturdy boots" or is it like an archer losing their bow or a wizard losing their spellbook? Because that is what I'm talking about.
It is literally everything they owned, including their physical form. The character went from a physically strong magically-powered construct with rocket fists, teleportation powers, and lots of other tricks to a sentient cloud of expanding and cooling magical plasma. They got back
a body relatively easily, but the body has none of their powers and just lets them interact with the physical world again.
Well, ok, that is that one specific game?
PBtA is short for Powered By the Apocalypse; it is not one game but a framework/engine for many games. It shares design elements with tons and tons of games that don't share its basic mechanics as well. But frankly, I don't see the need to educate you on the subject, and this isn't the place to do it anyway.
But if you have shared power and control...equally...then each player would have veto power. That is how "shared" works.
"Shared" does not entail "shared equally." When the Conservatives and the Lib Dems ran a coalition government in the UK, they shared power, but there was no doubt that the Conservatives had
more power than the Lib Dems. Nor does equal sharing of power entail that everyone can veto. It might be that no one can veto. It might be that different players can veto different things. It might be that some things can't be vetoed and others can. A veto might involve a vote—anyone can propose something, and if a majority agrees, that's what happens.
And one game might involve more than one of these alternatives. I'm thinking here about systems where the party has some shared resource which a character can spend to benefit themselves. For example, the Outgunned system gives players a limited number of 'Plan B's' which can be invoked to 1) essentially guarantee success at a single action by a single character or 2) introduce a major narrative twist, like a fully armed helicopter gunship showing up to provide you covering fire in a risky firefight. Any player can spend a Plan B whenever they want, but to do so, they have to propose it. Then, if most of the other players agree that it's cool, it works. If they
don't agree, the player who wanted to use the Plan B can go ahead and use it anyway—but as a consequence, they're not allowed to use any more Plan B's for the rest of the campaign, and they don't get any benefit from a Plan B used by anyone else either.