When doctors/scientists say a new variant has become the dominant strain, what happens to the earlier strains?

Do they gradually disappear altogether as the new variant out-competes them for human hosts or what?

basically...yes

So, then, Omicron is more contagious, but far less virulent than Delta, so it is actually good news if it eventually eliminates Delta--particularly if Omicron burns out as quickly as the South Africa experience suggests? Or is that overly simplistic?

IIRC, isn't that the typical profile for viruses--more virulent early strains gradually displaced by less dangerous ones?

National news now confirming my amateur assumptions. We may be on our way out of this mess.