The catch is: a phone has a much smaller sensor, so at the same f-stop, across the whole sensor less light is gathered and consequently, you have a weaker signal.
f-stop doesn't mean much other than the maximum that the aperture for that lens can open.
It doesn't indicate lens or element quality, or aberrations. There's a reason that pixel peeping, gear games, and reviewers are so prevalent in high end photography.
As a simple extension to this, most of my lenses work better a few stops before maximum f-stop.
So, yes, but no.
For the rest - yeah, f# is just one of important specifications.
The aspects you are now referring to are about the lens quality. Yes, I would expect a real camera lens to be much better than the lens of an iPhone. There is no doubt about that. But in the posting I answered to, you spoke about the comparability of aperture values.