Yes, RNA viruses are challenging, and respiratory viruses are challenging. By the way, poliovirus is also an RNA virus, and it has a pretty high mutation rate too. This is also contributes to the probability of getting vaccine associated paralytic polio from the oral attenuated vaccine. (The Sabin version.). The Sabin oral vaccine has mutations introduced that make it so it is not neurovirulant. (But, as the crippled virus replicates in your gut, there is a small probability that it will acquire the right set of reversions to make it neurovirulant.) An advantage of attenuated virus is that the community gets an immune boost too.
The inactivated Salk vaccine was developed first, and is typically 90% effective after two shots- better after more. But, to make that vaccine back in the 50's they did have to sacrifice a lot of monkeys. There was also some manufacturing quality control problems where some vaccine doses we're contaminated with highly infectious virus. Not good. They've fixed/improved the manufacturing issues. The inactivated vaccine also doesn't elicit as strong of intestinal immunity as the attenuated vaccine. Over time there have been improvements in the protocols too, and vaccination schedules used to include a mix of the inactivated vaccine and the attenuated. With the eradication campaign, the oral attenuated vaccine will need to be stopped, but it is still used in other countries.
By the way, vaccination will have absolutely no effect on the mutation rate of the SARS-CoV2 virus. As long as the virus can replicate, it will make copying mistakes - and it will also recombine with other SARS-CoV2 genomes in the infected cell. At some probability, some combinations of changes could alter / reduce the effectiveness of neutralizing antibodies.