What's wrong with having fewer public companies?
There's really nothing wrong with it from most entrepreneurs' POV: they build something people want, they get paid for it.
The problems occur at the margins: the businesses that could be started with enough outside capital but can't be bootstrapped off initial cash flows, or the small investors that are perfectly capable of doing due diligence on companies but are banned from investing because all the attractive investment targets are private. It's really an opportunity cost issue: things work okay, nobody gets visibly screwed over, but all sorts of little transactions that would make life better for everyone never take place.
This is basically the story behind investment trusts, mutual funds, and hedge funds. Back in the 20s, everybody put their money into investment trusts. They got screwed by the Great Crash, so the government put all these restrictions on public investment vehicles (can only invest in stocks & bonds, can have no more than 1.5% of assets in any one security, etc.) and the trusts were reborn as regulated mutual funds.
Then people realized that because mutual funds were so regulated, they were leaving money on the table, and all these alternative asset classes like commodities, timber, derivatives, venture capital, etc. were ripe for the taking. So they created a new class of investment vehicle, hedge funds, without the regulations but only open to people who supposedly know what they're doing.
Now ordinary people are investing in hedge funds indirectly, through funds-of-funds and pensions, and they're getting screwed. So there're calls to regulate hedge funds now.
Financial markets treat regulation as damage and route around it. Unfortunately, they sink many suckers in the process and create demand for new regulation, and so on.
It's hilarious because hedge funds are a scam (based on traditional 2 & 20 fees alone). Then someone creates fund of funds, which is a scam of a scam. And people are dumb enough to buy it.