Earlier quoted context omitted.
Evolvability can also evolve away too. For instance, a gene that decreases the mutation rate to 0. Most mutations are harmful, so any organism with the gene will be more likely to have successful children. And eventually the gene will become dominant and there will be no more mutations. And evolution will stop.
What you say is fairly hypothetical, since the way genetics works at a fundamental level prevents this possibility. You are also oversimplifying by not distinguishing local and global success. Locally, this gene will be successful. Globally, some mutations will be beneficial , and the children with those mutations will be more successful. The gene may become "dominant" (and then gain the beneficial mutations through…
>it will not achieve a monopoly and not remove the existence of evolution.
Yes it will. It's easy to do simulations. Statistically the children of the organism with less mutations will have an advantage. Eventually the gene will reach 100% of the population. The population will stop evolving and eventually go extinct.