That is a healthy skepticism! I definitely would not counsel people to do it with primitives in general: it just turns out that a PRF doesn't have a complicated

That is a healthy skepticism! I definitely would not counsel people to do it with primitives in general: it just turns out that a PRF doesn't have a complicated API and HMAC is bulletproof. More or less the only design criterium that comes to mind that is critical is "don't do anything before you validate the MAC", and that design guideline is hard to break when you use the suggested approach.