The IPO company is a one-time customer
Sort of, but not really. The IPO company is ONE customer and if other pre-IPO companies see the udnerwriter “ripping off” the company, then they will take their business elsewhere. The underwriter needs to find a price that can make both parties happy, and even the best may find that difficult at times.
Also, having a neighbor with family money at Goldman Sachs, I know that clients are often forced to take mediocre IPOs in order to be eligible for the great ones, so both sides have to give a little bit.