It's simpler: If this stock was such a great deal that everyone would buy the it over anything else, then clearly Anthropic had set the price too low.
I would actually argue that if they price the IPO too low, people would assume they are not confident in their company and the whole AI sector would sink.
Almost like a "Veblen good" type investment.
They basically have to price it at an unreasonable valuation so that people curse them while they take it. There's no way around it.