Really if we want to break this cycle we need one important thing: a punishment for daring to propose it. Harsh but I can see no other way.

I don't think it's possible. The politicians needs something to talk, a psuedo-legged horse to ride on. The Mega Corporates need something to do, a psuedo-promise to show that they're not only abiding to the policy-makers and to do good by the users.

are there any studies that show banning encryption would actually result in more criminals being caught?

No, but that doesn't cancel the desire for law enforcement to pry in unbreakable encryption.

There is ample evidence that breaking or backdooring apps or devices (more or less specifically) targeting criminals, allows the cops to roll up huge crime networks. These are expensive and time consuming one off operations.

Main stream messaging apps like Signal and Whatsapp of course rely one very similar technology so it's probably safe to assume some illegitimate stuff is happening there. I wager that finding those criminal messages in practice has a more serious issue beyond encryption: there is far too much data.

And even if encryption were banned altogether, the criminals would surely find a way to whispers their mischiefs in stenography.

It would*

*If the criminals would stop using encryption now that it's banned. Alas, criminals sometimes break laws

You look for your keys under the lamp post not because they're there.