The number of variants that arise is proportional to the amount of the virus in circulation. Vaccination reduces the number of variants.
I'm not sure where you get this information, but lets look at the way I came to my uneducated conclusion.
I'm an ex mainframe systems programmer, so I tend to have an enquiring mind, and I like to get to the root of things. Corona Viruses have been around since the 1930s, and there haven't been many variants until fairly recently, now we suddenly seem to have variants almost every day. So I wondered what was causing this. This led to to try to discover the way that viruses replicate amongst other things. Viruses don't have a sex life, but nature does need to find a way to encourage them to mutate and cope with attempts to destroy them. There is a fairly simple process to allow this. A virus doesn't create a complete clone, but builds half of a new virus, and then goes away. The second half of the new virus is crewated by a different virus ( or possibly the same one). If both viruses are of the same strain, then the new virus will probably be a clone. Of course there may be errors, but there is a good chance that these will be non-viable. If a cell contains more than one strain of a virus type, then the second half combined with the first half will create a variant. Vaccination creates different strains of the virus, and is focused solely on the spike protein. Natural selection will tend to give preference to variants with modified envelopes that can avoid selection based on a simple spike protein check. Natural immunity will check all 28 of the proteins on the envelope, and this means that variants are more likely to be detected and destroyed.
This is the reason that all previous medical advice states that vaccines should be used as a prevention and not a cure. They should not be used where a virus has become endemic. This is the first time when this advice has been ignored. Also, medical opinion advises that vaccines are not needed where strong natural immunity is present. Again, this is the fist vaccine that goes against this advice.
It is obvious that vaccination against Covid has nothing to do with health, and everything to do with wealth transfer and population control.