The framing that each model moves risk to a different party is the clearest way I have seen this explained. Fixed price moves cost risk to the provider and change risk to the client, and most arguments about contracts are really arguments about which of those two someone forgot.

Your warning that quality is the hidden variable on fixed price is fair. When the budget runs short, tests and edge cases go first, and written acceptance criteria are the only real protection. The onboarding rebuild example also shows nicely how the same change plays out under each model.

We work fixed price at Ascendra Ventures, and the hybrid you describe at the end is close to how it works for us in practice: a short fixed scoping phase, then a fixed price for one clearly defined problem with acceptance checks agreed up front. Anything learned later becomes the next piece of work instead of a running change request.

In your experience, do clients usually value the discovery phase, or do they see it as paying for a quote?