Graham Lineham, sitcom writer behind several successful Irish and British sitcoms, wrote an article on this.
This seems the most important point (my bold):
Audience laughter, when it's deserved, acts as a sort of fairy dust that makes funny moments not just funny, but joyous. It also takes the edge off moments that otherwise might tip over into tragedy; imagine Basil Fawlty whacking his car with a branch or goosestepping around a hotel lobby to complete silence and you're imagining not a comedy, but a fairly grim account of mental collapse.
It's a stylistic thing that changes the tone of a scene. As the asker says, without laughter, MASH is quite a grim account of some of the horrors of war, which is interesting, but not what the creators wanted.
Contrast it with modern sitcoms that don't have laughter, such as The Office, Peep Show, Arrested Development, Curb Your Enthusiasm etc - these tend to be more like comedy-dramas with humour frequently based on tension, where laughter would kill the drama and the tension. Comedies that do choose to add laughter tend to be comedies that are lighter, sillier, or more knowingly over-the-top (especially Lineham's).
It's worth noting that Lineham's sitcoms, and I believe most sitcoms with a laugh track, are filmed in front of a live audience - the laughter is a genuine audience reaction that the actors can hear and are responding to, it's not "canned laughter" added in post-production. It's also usually taken from the first take, since that's usually the biggest and most genuine laugh.
He also gives some reasons that are specific to live audiences:
it pushes me to make the show funnier... Under the threat of such an unpredictable group of people, any line that doesn't get a laugh stands out like an old guy at a party.
There are some actors who come alive in front of a crowd, and if you've cast it right, there's an energy between cast and audience
A lot of the comic timing of sitcom actors in sitcoms filmed in front of a live audience is based on responding to the audience, which is part of the reason why it can be so painful to watch these when the audio track from the mics pointed at the audience is turned off: the actors are reacting to something that isn't there.