It might not "solve" the problem, but I'd expect it to significantly address the problem no?
I've heard much criticism of it being too heavy-handed, but I don't think I understand criticism that it won't improve security. Could you expand on that?
No. You seem to be implicitly arguing that that unsigned apps are inherently less trustworthy than PlayStore apps. That's a claim that needs to be proven first. And based on the huge amount of documented data exfiltration performed by Google-approved apps, I'm going to say that claim is false.
I'm arguing that a curation process that includes security review is likely to produce a more secure set of software. Admittedly it might be completely ineffective, but I think that's an unreasonable assumption. So some review is more secure than no review. Now I'm not saying "better", you could argue it's a false sense of security, but it's still more security.