This action still creates a new estimate which the client hadn't approved to get an invoice. By deleting the actual one that the client approved, its going to bring alot of confusion during discussions of the project as the client will be taking of a different estimate which you eventually deleted but have a copy of the items in another estimate. The sanctity of the estimate numbers to remain consistent in all client discussions is very important. It ensures both parties are taking about the same thing at all times.
Secondly, creating an estimate then deleting then creating another one under projects is still double work just to get the estimate under projects. I already spent so much time building the first estimate. For me in construction, that's about 30 mins an estimate, deleting all that work then doing it again isn't fair.