It's not how contagious it is, but how lethal it is.
There are colds that are contagious, but not that lethal and so have not really been a factor in recent years. A few versions of Covid (prior to Covid-19) also fit this area.
It is not to hard to understand why the more contagious strains are gaining momentum. As we got better at avoiding the earlier strains via vaccines, social distancing and masks, the only way for the virus mutations to keep infecting people were to find ways around them. It developed ways to infect people who were vaccinated by mutations, as well as mutations that made it easier to infect people despite social distancing being the strains that survived and grew.
If we are lucky, it also coincides with less lethality, but...not necessarily. We still have a version of the Spanish Flu today, and in some ways it may be just as, if not more, contagious. I do not think it is as lethal as it's original strain, which is why we don't make as big a deal about it today. We can HOPE Covid-19 follows this route, but it's hard to say.
It is a hope because strains which keep the host alive longer, and have a longer period of spreading, normally are more effective at remaining around than those that kill the host or kill it quicker. Thus, a less lethal version can be hoped to eventually be the winner in the virus contest.
I think Omicron originally was seen as less lethal than earlier strains, it was the strain that had a combination of Delta and Omicron that got people concerned. So far, it also has seemed less lethal, mostly due to prior infections and vaccination.
New strains are coming up though, We are still in the wild west of Covid. Worse, infection from Omicron doesn't necessarily carry immunity to other mutations of Covid.