They tried that with the FireBee (Atari Coldfire Project), and the end result is that they have a pretty neat piece of hardware that's decently fast and a bit spendy and not very compatible with the ST.
You could do some things to make it more compatible, but you're slowing it down to do that. You could conceivably make it near 100% compatible by having a layer (FPGA?) in front of the CPU, but if you're going to do that, you probably just want to use an FPGA or a more compatible CPU...
It is a very neat project tho and shows you how kual the tech is (they have some version of TOS running, it looks like)...
But the minimig and natami vids show they are much more compatible already..