In the particular conditions we created in 2020, the Rhinovirus was better able to spread than the Flu. Why?
Because people were on the lookout for fever (and other things like continuous cough etc). Flu causes fever, and anyone who got a fever and was sensibly-minded would self isolate at least for a few days until they got test results or until symptoms abated. Whereas Rhinovirus is much less likely to cause a fever, so people twig that they've 'just got a cold' and carry on going about their day.
Especially for schoolkids - if they've got a fever, they're kept at home. If they've just got a snotty nose then they're likely to still go to school.
So Rhiniovirus was able to fly under the radar whereas Flu wasn't.