The frustration aimed at Discord et al is largely misplaced. I'm sure these companies don't mind gathering extra data about their users, but the primary impetus for age verification is government legislation. Moving to alternative platforms is not a long term solution because it's attacking the problem from the wrong direction.
I agree that government legislation is part of the equation, but I don't agree that moving to other platforms is not a solution. If Discord were to witness a significant exodus of paying users because of this new verification process, they would probably start fighting the fight themselves.
That said, I don't expect this to happen, switching is very hard for many reasons.
You act like public opinion has no bearing on politics.
Historical precedent: prohibition.
Alternate future: the big websites start losing billions because people just use the internet less or not at all because it's a hassle with no return, and tax revenue drops. Then the politicians start to worry.
Even in the absence of democracy, public opinion affects politics.
Yes the same outraged users were totally fine with giving Discord all their personal conversations.
Not just government legislation, but also lawsuits. I'm confident that Discord is a hotbed of all kinds of abuse and inappropriate / adult content, a lot targeting younger generations, and most of their resources are spent on that. Age verification doesn't solve that problem per se, but it makes things a bit easier.
The challenge with "protect the children" is not only evildoers targeting them, but targets actively seeking things out. They'll be the first ones looking for ways to circumvent age verification.