There are services like that for Mastodon [0]. But a provider that lets you host from a choice of e.g. mastodon, pleroma, lemmy etc would be interesting.

[0]: https://masto.host/

masto.host has a great deal of restrictive, somewhat arbitrary content moderation policies for what is basically just a server host[0].

Since that the original problem is that admins may want to override built-in censorship policies to suit their instance's needs and values, I don't think an even more censorious centralized authority is a great example of a solution.

[0]: https://masto.host/tos/

I have no affiliation, nor a recommendation. Just noticed that they do provide that service.

Using any hosting provider is ultimately a risk compared to hosting yourself, that's the price you pay for not having the know-how to host it yourself.

And even if you do selfhost, cloudflare may wake up one day and say "nah".

Masto.host is run by one of those people who put inflexible ideology ahead of the wants and needs of their users. That is ever a concern when having a third party set up and manage everything for you.

Does that one click also edit the source code?

I suppose users could apply patches and alter configurations? Caveat Emptor: we do not offer customer support for altered source/configs.