3 to 3.5 should be the minimum IMO.
Mainly because there are a few Hards that are 3.5. These mostly are a low BPM. But they feel much more like a Hard than a Normal.
Most 3 to 3.5s are often only that low because A. low BPM, B. they have spurts of beats, then a second or three without beats but not long enough for a break, then repeat, whereas 4+ star maps are constant throughout, or C. a combination of those two.
Point is, they often aren't significantly easier when you are actually playing them.
Of course, it's mainly maps from around the time I joined or before that are like this. But even the easiest Hards are 3.5; can't think of one lower than that. 3.5 or 3 should be the minimum IMO, just because of a few more modern exceptions, and some old classics.
I do think that the judge-chosen maps should have a higher star minimum due to this very reason, though. 4.5 seems about right.