The cases where such a cpu would be efficient are already the places where a normal cpu is extremely fast. So it would also fail in the same ways, pipeline stalls and all. If you need to wait for the answer to one computation to know what to do next any additional cores won't add speed.
A good part of the complexity of current cpus comes from features like branch prediction, speculative execution and so on so removing features wouldn't make them drastically simpler.
Many of the truly rarely used instrucctions aren't build in hardware and therefore don't contribute to the complexity of the cpu anyway. Others are rarely used but add huge speed boosts for important special purpose tasks, think os kernel.
A good part of the complexity of current cpus comes from features like branch prediction, speculative execution and so on so removing features wouldn't make them drastically simpler. Many of the truly rarely used instrucctions aren't build in hardware and therefore don't contribute to the complexity of the cpu anyway. Others are rarely used but add huge speed boosts for important special purpose tasks, think os kernel.