Good question. So, how would we know? Well, you could look straight up at the NYSE listing data, which shows U.S. [non-foreign] NYSE listings peaked at 2,722 companies in 1998. Today we are 15% lower, with "only" 2,315 NYSE-listed companies, which represents 412 fewer firms.
That's kinda interesting, but it doesn't tell you much. Maybe we had too many listed companies in 1998, and maybe we still have too few now. It's hard to know from this data.
Just for fun, here's another approach. How about normalizing the number of listed companies in any given year against [real] U.S. GDP? That way you've got something to test listings against. The result? See the following figure, which seemingly shows that, if anything, we are over-IPO-ed.