Yes, this should totally be attempted. All the stack manipulation opcodes could be dropped if we just made (nearly) everything use 3-address codes, e.g. ADD would take the names of three registers, left, right and result. The compiler would keep track of which registers contain a live object (for reference counting) but that can't be much more complicated than checking for stack under- and over-flow.
Also, nothing new indeed -- my first computer (a control data cyber mainframe) had 3-address code.