No doubt, trying things on the fly and in the middle of an emergency is not something take lightly. There will be an urgent need for mental health care.
That is not the reason per se, as obviously in both RNA and DNA viruses the genetic material needs to be amplified and both can incorporate errors. There are a few mechanisms, such as polymerases, exoribonucleases and other enzymes that may proofreading functions and thereby reduce mutations. Coronaviruses have such functions and therefore have a lower mutation rate compared to other RNA viruses and put them in the upper range of DNA viruses (~10^-7 - 10^-6 for SARS-CoV, I believe similar for SARS-CoV-2).
The mutations are not necessarily in the spike protein, if that is what you are asking. Mutations are going to accumulate in areas that do not inhibit the ability of the virus to propagate. In fact, some of the mutations observed are "silent" meaning that the codon changes, but as a whole still codes for the same amino acid (this includes mutations in the spike and nucleocapsid genes). These mutations are unlikely to result in significant phenotypic differences.