OK, my ignorance.
So, do species of roaches that lived with dinosaurs no longer exist now? If so, how old is the oldest roach species?
Well, roach is only an arbitrary example. This question may apply to any species. The point is to find out how resistant is that species to mutation. If it is longer than a few million years, then we need to ask how could it be so resistant, if mutation took place randomly and constantly. What determine if a mutation would be accepted by the life of not? Environmental stress? Didn't those species receive enough environmental stresses over millions of years? How much environmental stress is needed to make a particular mutation accepted?
With regard to cockroaches, many species have evolved quite remarkably. We have species of cockroach where the young feed on secretions from the anal glands of the parent. We have termites, which evolved from ancient roaches.
Saying a species is 'resistant to mutation' is not very accurate. Think: you have one million ancient cockroaches. One of them acquires a mutation. All of them reproduce. Now you have one hundred million cockroaches, only a few of which have that mutation. Nothing is killing the ordinary cockroaches off before they reproduce, so they continue on. In the course of a few generations, the mutation is thoroughly diluted within the population - only a few cockroaches have it.
Or it is equally possible that a small population of these cockroaches, including a few that have the mutation - let's say it causes more waterproof egg cases to form - ends up living in a swampy area. A lot of eggs don't make it, they get mouldy or the case doesn't protect the eggs from water damage. But the mutated cockroach eggcases almost always hatch. Within a few generations, most of the cockroaches in that swampy area are descended from the few with the mutation. They still look exactly like the other cockroaches, but they have evolved.
But back in another habitat, there is still nothing preventing cockroaches without the mutation from merrily laying eggs as usual, and this prolific, widespread species is likely always able to survive in a friendly habitat somewhere in their range.
Modern cockroaches which are similar to ancient cockroaches are an example of what has turned out to be a very successful bodyplan and set of habits. And yes, there hasn't been enough selection pressure to eliminate these cockroaches, many mutations have no doubt occurred, but most are diluted in the larger population.
Nevertheless, many populations of cockroaches
have evolved due to mutation and selection pressure, so we have termites, and hissing cockroaches, and huge palmetto bugs, and little beetle-like German cockroaches.
And even those common cockroaches, looking so much like their ancestors, there are minute differences, and they evolve pesticide resistance regularly.