The rules aren't terribly stringent, and if you can stay above this then it might work.
The problem is no underwriter would take an IPO for a million shares at say $10/share. It's just not something that they can make money on.
This would require a new type of low cost underwriter.
Alos remember, the reason why we can set a price on the stock is that we know the float ahead of time and we can estimate what the company is worth.
How can you price a share if the amount of tradable shares is materially changing each day?
If you're offering a small fraction of the outstanding float, you don't need an underwriter because you've elected to reduce your risk. If markets are unfavourable, you raise less. Oh well. You've kept plenty of shares to try again next time.
We need to get over this "go big or go home" mentality.
With out an institutional investor( Buy side) your stock will have a hard time getting any traction.
If the stock won't trade, they won't let it list, period:)
Also each time you sell shares in an IPO you need to have people make lots of calls to institutional and other investors to determine the demand and thus proper pricing and supply of new shares. Having to do this everyday will be expensive. You (as a bank managing the IPO) also probably don't want to pester fund managers too much (They have to take care of other stocks in their portfolio, too), otherwise you'll have trouble doing IPOs for other companies.
EDIT: I take that last sentence back, it seems like they really want those IPOs regardless if the bank is a vampire squid, or not.
Underwriting does get you what it says, a guarantee that they will take the whole allocation, which was the original reason for underpricing. There have been a few cases where underwriters lost a lot of money (eg the BP floatation in the UK), but usually the underwriting fee is pure profit, especially if you can get the launch undervalued, and there are usually options that make it pretty hard to lose money (as with Facebook).
I'm a firm believer that releasing all the shares and allowing the market to decide what they'll pay for the stock, based on their own valuation method, is the most efficient method.