For one thing, barrier to entry is not a security feature. Malware has made its way into paid app stores.
I think someone running Linux wants low barrier to entry as a reason to use the system. They want a system built by communities and not by corporations with walled garden toll booth business models.
But this point is extremely weak either way when you compare to the Windows barrier to entry which is effectively zero. Or you can compare flatpak to Mac users installing software with Homebrew.
I think if you look at flathub there are very good explanations on each piece of software regarding whether the author is verified, what the license and code availability status of the package is, and which permissions are being used when installed. It seems
to use relatively strong language to describe permissions features as potentially unsafe.
Flathub is VERY transparent which packages are not verified and unlike system packages they come with sanboxing which if correctly configured (also transparently displayed) can mitigate malicious access.
With distributions packages, there's a bigger barrier to entry which is at least better in avoiding sneaky malware from easily creeping in.