Technically feasible, indeed. When Microsoft and Sony created the Xbox and PS4, they followed that approach, and it's likely there are developer configurations available for those systems. However, you must enter licensing agreements, NDAs, and pay development costs. The platforms also use DRM, requiring specific tools and keys to operate. In practice, it's not straightforward.
The issue is similar to why you can't install a laptop HDD on a desktop without it booting properly—drivers don't match. Consoles also use different hardware, like PowerPC, which adds another layer of compatibility problems.