Solid Hardwood, Engineered and Laminate Flooring - New floors over old

We are in the process of laying new hardwood floors in the new remodeled part of our house and then will continue with the old part of the house. We are using 2 1/4 x 3/4" red oak. In the old part of the house there is already 60 year old 1 1/2" x 1/2" red oak that has seen it's last sanding, so we will replace it. That was the long way to my question -- is there any reason why we shouldn't just put the new wood down over the old? It is in good shape (other than beat up and can't be sanded again) and the 1" x 6" subfloor is also still in good shape. We're hoping the save the trouble of tearing it all out. Thanks for any advice or suggestions.

Doing that usually leaves a bump at transitions to a different floor, but other than that, no reason not to.