The problem is the precedent, globally, of killing encryption is well documented. There is no good solution that doesn't harm everyone. Here in the states, the Clipper Chip [0] was the textbook example of politicians trying to legislate mathematics. You wouldn't even be able to do something like "give us a copy of your private keys" because then you'd go down the path of playing wackamole with every distribution, every slightly recompiled GnuPG, etc. It's an intractable problem. We, in the US, would've gone a long way by stripping Dorothy Denning's CS PhD from her [1] after her outspoken support of such measures. Instead she has received many awards for her "work" in the field of rights erosion.
The US seems to have settled on making attempts at Clipper 2.0 every decade or so. In the meantime encryption is considered a weapon legally which is how the DAs get their fill. Germany appears to have flat out opposed it...but it's only a matter of time. The EU will force them to bend the knee because historically they always have. It's a fantastic effort. Unfortunately, done by one of the biggest pushovers in Europe.
There's no hope for the technical among us. The people with power who do understand, the technocrats, are behind these efforts. The people that don't understand are behind these efforts. It's only the intractability of the problem that makes legislating it dangerous. Once someone clever enough makes it tractable there won't be encryption anymore. Pre-crime is the way the world has worked since 9/11 and encryption is #0 on the list of things to legislate to death. In the US, there are likely hundreds of billions of taxpayer dollars being spent to store every last bit of communication in Utah for this eventuality.The EU has a similar program. Those tax dollars have to be justified somehow. So when you ask "who would support this"... just follow the money.