I can see most of the benefits, primarily, it makes it possible to compile to C using it's normal calling convention. I.e., instead of trampolining thunks in the heap, most calls are translated to regular calls using the stack (the machine's calling convention) and closures are build in the heap on demand.
Translating to an abstract machine which uses a stack and heap, instead of just a heap, isn't a trivial move. Though, theoretically, combinators are easily translated to a stack/heap machine, at the moment, I fail to understand all the ramifications.
Is it true, and why would this be the case, that Clean's ABC machine is as fast as optimized native code?