They can try the same as they can pass any other law. Of course, whether or not practically they can do it is another issue altogether...

Given the opportunity, most governments would. Just look at the US's attempts to force phone OS vendors to include backdoors

They would just have a single state-run CA and ban all E2E messaging apps from app stores. Only state employees would have access to an E2E messaging app that would only use govt certs from the CA. Any apps that continue to operate outside of an app store could have their domestic servers seized and anything foreign would be blocked by all domestic ISPs. The govt could allow for civilian apps to use weak encryption as some sort of compromise but anything the govt can't crack instantly would be banned. It would require a Great Firewall-level of control with the govt playing whack-a-mole for a while but with enough time and money, civilian E2E would be near impossible. Fortunately, this is still a pipe dream for even the most extreme statists but if large corporations can come around to the idea of giving the govt an unlimited backdoor to their internal communications, say good bye to any/strong encryption for the average person.

This level of planning is like the US govt outlawing all guns tomorrow, it just isn't going to happen any time soon since not only are gun-owners usually not the type to want to give up a gun, the prevalence of gun ownership is so massive that it would take equally massive resources to run a completely successful confiscation program.