Startups don't make sense as thin wrappers around another company's product when that company is aggressively expanding that product is a core offering that the vendor is aggressively working to provide as an integrated solution for as many markets as possible, which very much applies to OpenAI offerings in general, and its chat models especially.
A wrapper that also leverages some exclusive special sauce data, algorithm, etc., for which you have a real moat as a key component, that makes some sense. But just a thin wrapper around GPT? That's just asking to have your market eaten by OpenAI.
It might make some sense for products where the vendor is a stable, steady-state infrastructure supplier for many markets without any evident interest in entering the same market as the startup, where the uncertainty across markets that they would create by specifically targeting your startups market would hurt them more with their established customers than they would gain from your niche, but even that is risky because it requires lots of potentially-erroneous assessments of how the vendor would expect their other customers to react to them acting in your market.