Yes, I think governments love centralisation of control in very few hands. It gives them far greater powers than they would otherwise have, both technically and legally.

"Harmful" content has significant overlap with freedom of speech, so governments find it hard to ban directly. But when there's a big corporation facilitating access to that content, then it becomes a clear case of "evil capitalist profiting from harmful content - corporations need to take responsibility!".

When a government doesn't like end-to-end encrypted photos and cloud drives, all they have to do is issue a secret order telling Apple to disable it.

And when people find workarounds for intrusive and insecure age verification methods, what's better than a total sideloading ban to regain control?