I don't think they should. That's not what a degree is - a degree is a qualification awarded by a university.
Professional qualifications on the other hand.... are best studied for whilst working but I would still think better monitored and awarded by a professional body or institute rather than individual companies, otherwise there would be no way to compare one qualification to another. You would either have to requalify every time you moved job, or stay with the same company for your whole working life....
As for the quality of education, that seems like a completely separate question to me!
Practical experience is important but it is the icing where the university degree is the cake. Degrees offered by companies could lead to an incosistency in the quality of education in particular fields.