It's already well on its way, from what I can gather.
One frustrating aspect of the reporting for me is people talking about "more infectious" variants without describing whether or not they are more or less dangerous. In general, the virus putting more work into being infectious is good news; it generally comes at the cost of being less dangerous in other ways as it hyper-optimizes into replication rather than anything else. We should expect and want to hear about "more infectious" variants, which double as natural vaccines to some extent against other less infectious, more dangerous strains still using the same external protiens.