"Let's just assume that the investment bank's only goal is to accurately predict the demand for a new IPO"
I'd say that their main goal is to make sure that the shares are all sold at a price that everyone is happy with - the management team of the company going public is heavily involved in all the steps on an IPO.
Like taking VC money, nobody makes you go public and both are things to do with your eyes wide open.
technically speaking the SEC does not force you to go public.
The problem most people refer to: if you have over 500 shareholders of record, you have to make a lengthy filing which is almost as onerous as going public. Hence, since the incremental effort isn't that much, most companies in that position go public. There's technically no compulsion to do so.
I'd say that their main goal is to make sure that the shares are all sold at a price that everyone is happy with - the management team of the company going public is heavily involved in all the steps on an IPO.
Like taking VC money, nobody makes you go public and both are things to do with your eyes wide open.