It happens all the time. I have been involved in such businesses, and there are public examples[1].
Entrepreneurs who don't code do not need technical co-founders. There are plenty of talented firms and solo developers with product management chops who will collaborate with you to build a product. The entrepreneur pays a fair rate and the service provider delivers a solid foundation on which to pursue the business.
Many if not most of the folks looking to jump into bed with a technical co-founder they have no existing relationship with are doing so because they don't have adequate capital. Undercapitalization is one of the top reasons new businesses fail, so most equity-only/deferred comp. technical co-founder opportunities are unattractive from the start.