Don't hate the politicians who keep pushing this. They're just trying not to get fired. And the surest way to get fired in a western country right now is to be seen doing nothing about the terrorism problem and then having terrorist acts committed under your watch. So the politician asks the security forces "what can we do to stop terrorism?" Security says "get us access to messages of terrorism suspects". Seems reasonable, let's go ahead with it.
Yes, we know that it doesn't stop with terrorism suspects. Then law enforcement wants to read the messages of drug kingpins, then drug suspects, then shoplifters, then jaywalkers, then everyone, just to be on the safe side.
But as long as people are told that they need to give up some privacy in exchange for security, they'll take the latter every time.