Sideloading is very possible on iOS and there's an entire subculture surrounding it.
As somebody put it, Google goes after others without cleaning their own house first. It's just abuse of power at this point.
Don't mistake obscurity for security. FDroid isn't the size to even be noticed by problems that Play Store and AppStore are dealing with.
Now, it might be a problem of vetting at scale or malware being really subtle, but if that's the case Google should focus on improving their process before locking down Android for "security".