This is just such a naive view. "We can prevent programs from crashing by just taking care to stop them when they do bad things". Well, sure, that's why you have a kernel and userland. But it turns out, some things need to run in the kernel. Or "just deny permission". Then it turns out some programs need to run as admin. And so on.
There is a generality in the halting problem, and saying "we'll just kill long runing programs" just misses the point entirely.
Likely what will happen is that you will kill useful long-running programs, then an exception mechanism will be invented so some programs will not be killed, because they need to run longer, then one of those programs will go into an infinite loop despite all your mechanisms preventing it. Just like the crowdstrike driver managed to bring down the OS despite all the work that is supposed to prevent the entire computer crashing if a single program tries something stupid.
Linux and windows are completely monolithic kernels; the crowdstrike agent isn't running in a sandbox and has complete unfettered access to the entire kernel address space. There is no separate "the kernel" to detect when the agent does something wrong; once a kernel module is loaded, IT IS the kernel.
Lots of people have indeed realized this is undesirable and that there should be a sandboxed way to run kernel code such that bugs in it can't cause arbitrarily bad undefined behavior. Thus they invented eBPF. That's precisely what eBPF is.
I don't know whether it's literally true that someday you will be able to write all possibly useful kernel-mode code in eBPF. But the spirit of the claim is true: there's a huge amount of useful software that could be written in eBPF today on Linux instead of as kernel modules, and this includes crowdstrike. Thus Windows supporting eBPF, and crowdstrike choosing to use it, would have solved this problem. That set of software will increase as the eBPF verifier is enhanced to accept a wider variety of programs.
Just like you can write pretty much any useful program in JavaScript today -- a sandboxed language.
You're also correct that due to the halting problem, we'll either have to accept that eBPF will never be Turing complete, OR accept that some eBPF programs will never halt and deal with the issues in other ways. Just like Chrome's JavaScript engine has to do. I don't really view this as a fundamentally unsolvable issue with the nature of eBPF.