von neumann architecture fix

Everyone knows about the von neumann architecture and the bottle necks that come with it.  I have an idea though.

Why not have two separate sets of ram, one for memory and one for programs?  Both would be exactly the same, both able to read/write/store code like normal ram, but while one ram is executing it can use the other one for memory storage eliminating the bottle neck.  Also all programs would be backwards compatible because a program can still run on a single side of ram and leave the other alone.

Would this be an easy solution or am I missing something here.

Almost all modern CPUs use a Harvard architecture internally, with separate instruction and data caches. The external interface is von Neumann for a number of reasons including compatibility and conceptual simplicity.