The actual question either IS why animals don’t take intentional actions regarding their DNA, I.E. ‘cheat’, or the answer is so obvious that it doesn’t need a thread.
The specific mutations required to look like something poisonous are a matter of blind luck. That they might be selected for afterwards, and it’s been explained already why they might not be, does not change how likely they are to appear in the first place.
No, but it does change how likely they are to confer a survival advantage when they do appear. Which is what the OP was asking.
Just to be slightly pedantic, those mutations might not entirely be down to blind luck. Sticking with the bee/wasp mimics, it’s possible that bright yellows abdomens are a common byproduct of insect development (perhaps analogous to the way leaves of certain trees turn yellow in autumn.) In most insects this is disastrous as it increases their visibility to predators. Selection then works against the tendency. But in venomous insects and their mimics it is advantageous. I don’t actually think this is the case, but it’s a simple example of how particular patterns and colours could crop up again and again non-randomly.
Also, if the question really is (as I interpreted it) ‘why don’t we see more mimicry in nature?’ I think it’s a perfectly good question and not obvious at all. Sometimes asking a question that seems obvious can yeild unexpected answers. Why do things fall to Earth? Because they’re heavy, duh.
If you look closely at the abdomen of a wasp, you can see that the stripes are actually composed of a yellow fringe on one edge of each segment of the exoskeleton - it’s probably a simpler mutation than you might think for something like this to arise because the segments are to an extent, repeats of the same construction, so there are cases where one mutation or one small group of mutations plays out multiple times on the insect’s body - e.g. stripes.
Plus, the vast reproductive capacity of insects, and the short generation cycles mean that nature has had very much scope for experimentation. It doesnt have to work every time or even every millionth time.
Evolution doesn’t do what is best, it does what works. So as long as the species lives long enough to reproduce, it has no need to further evolve, just to “fine tune it.”