Well, if the above were true, then you would have strong evidence for evolution. However this is not the case. The coelacanth, the shark and many other living species have not changed in over a hundred million years. The cianobacteria has not changed in over 2 billion years. Evolutionists even admit that frogs, lizards, etc. are the same from hundreds of millions of years back. So clearly, by your own terms, evolution is false.
Yes, some species are fairly stable. But your claim is that all species are stable. Giving a few examples of stability is not evidence for your proposition, especially given the numerous counterexamples. Indeed, by implicitly accepting modern interpretations of the fossil record, you have opened the door to the counterexamples.
Do you even believe that any fossils are that old?