I like that, but that would indicate an antigen drift, with similar mutations. I think what we see in reality is an antigen shift with the virus finding a new reservoir, probably in domestic animals that have very close human contact. The mutations are to similar to leave it to parallel evolution
The key drivers that make viral (or indeed any disease agent) mutations successful are firstly, infectivity, second, antibody evasion, and lastly relatively long host survival. The virus spike protein has a relatively small deck of cards to shuffle, so it is no surprise that the same or very similar mutations should arise independently in any sufficiently large group of hosts.