Star Trek and Stargate both go by the premise that “anything that can happen does happen in alternate quantum realities.” It’s just that the characters from those realities assert that their version of reality is the only one that matters (which is an actual quote from Teal’c.)

The Prime Universe does still exist. As does the universe in Yesterday’s Enterprise and the Mirror Universe. To say that Prime does not exist is to say Mirror does not exist; and the Mirror Universe’s timeline, which is wholly separate from Prime, was accessed repeatedly by Prime characters (and vice versa) during the events of Deep Space Nine, not to mention TOS and Enterprise.