> Why would be in their interest something that can be used against them the moment the tide turns?

They are doing this to prevent tide turn and personally, I feel like if both/many political parties agree to something like chat-control and agree that they make it a bi-partisan issue, then they can fundamentally do it and the "they" would be constant

Also the "they" here also refers to lobbying efforts. The billionaires/millionaires/rich people might like these things solely because it increases the influence of govt. and thus the rich people as well

As an example, Let me present to you the UK censorship act which tries to threaten any and every website with a very large price which is very scary to many people who have thus shut down their services / websites to UK at large if they were a niche project/couldn't do it

Internet as we speak, would continue on to become more centralized. I feel like the idea here is that make internet so centralized that you can control the flow of information itself(I mean it already is but there are still some spots left like hackernews as an example)

Its also one step towards authoritarianism. This could be a stepping stone for something even larger which could have a more constant "they" as well but I have already provided some reasonings as to why they do that, simply because they can and chat control gives them a way to do mass surveillance which is something which to me increases the infleunece of both parties or the whole system massively in a way which feels very threatening to freedom/democracy making it thus dystopian.