That was true with Delta and earlier variants. Vaxxed people still are contagious for a shorter period than unvaxxed at this stage. But with Omicron, if someone who is vexed thinks there is no need for masking or avoiding close contact with friends and family, or strangers, even when they have symptoms then . . . that's why detected case counts have gone up so fast in places with high vax rates.
I used to say "Delta changed the situation" after June 2021. Now we are at "Omicron changed the situation" and that started in November 2021, not December.