Or is a by product of its former format, the live laughs with a crowd while filming?

This is the reason. Television comedy derives from stage shows where the audience sits in one direction from the stage.

A lot of early television comedy programming was often from variety shows, where the live studio audience is an important feedback mechanism for the actual performers. A standup comic needs a laughing audience to respond to (and often, so do other stage performers, including sketch comedy).

So television comedy comes from that tradition, and a live audience was always included for certain types of programs. Even today, we expect variety shows to have audiences. For example, John Oliver's show without an audience felt kinda weird while that was going on in 2020. And even some pre-filmed sketch comedy shows, like Chappelle's Show, would record audiences watching the pre-recorded sketches as part of the audio track for the broadcast itself, while Chappelle himself was filmed essentially MCing for that audience and those sketches.

So sitcoms came up on sets with live performances before studio audiences, just like sketch comedies and variety shows or daytime talk shows. That multi camera sitcom format became its own aesthetic, with three-walled sets that were always filmed from one direction, with a live audience laughing and reacting. Even when they started using closed sets for safety and control (see the Fran Drescher stuff linked elsewhere in this thread), they preserved the look and feel of those types of shows.

Single camera sitcoms are much more popular now, after the 2000's showed that they could be hilarious, but they are significantly more expensive and complicated to shoot, as blocking and choreography and set design require a lot more conscious choices when the cameras can be anywhere in the room, pointed in any direction. So multi camera still exists.