It’s impossible to prove that an arbitrary program, which someone else gave you, is correct. That’s halting-problem equivalent, or Rice’s theorem, etc.
Yes, we can prove various properties of programs we carefully write to be provable, but the context here is that a black-box executable Crowdstrike submits to Microsoft cannot be proven reliable by Microsoft.
There are definitely improvements we can make. Counting just the ones made in some other (bits of) operating systems, we could:
Rewrite in a memory-safe language like Rust
Move more stuff to userspace. Drivers for e.g. USB devices can and should be written in userspace, using something like libusb. This goes for every device that doesn’t need performance-critical code or to manage device-side DMA access, which still leaves a bunch of things, but it’s a start.
Sandbox more kinds of drivers in a recoverable way, so they can do the things they need to efficiently access hardware, but are still prevented from accessing the rest of the kernel and userspace, and can ‘crash safe’. For example, Windows can recover from crashes in graphics drivers specifically—which is an amazing accomplishment! Linux eBPF can’t access stuff it shouldn’t.
Expose more kernel features via APIs so people don’t have to write drivers to do stuff that isn’t literally driving a piece of hardware, so even if Crowdstrike has super-duper-permissions, a crash in Crowdstrike itself doesn’t bring down the rest of the system, it has to do it intentionally
Of course any such changes both cost a lot and take years or decades to become ubiquitous. Windows in particular has an incredible backwards compatibility story, which in practice means backwards compatibility with every past bug they ever had. But this is a really valuable feature for many users who have old apps and, yes, drivers that rely on those bugs!
XCOM games famously lie about percentages; they optimize for the player feeling good. Your actual hit chance is higher than displayed, repeated miss streaks are deliberately prevented, and so on.