It depends partly on what scoring system you're using.
Legacy System
If you're using a legacy system where the judges have to notice the hits, then any time they see the foot contact the pad they're supposed to score it. A basic roundhouse or snap side kick (not a pushing side kick) is 1 or 2 points, a back kick or tornado kick is 2 or 3 points, a headshot is 3 points, and a turning headshot is 4 points. (Sometime's it's 1 and 2 for roundhouse kick and back kick, sometimes 1 and 3, sometimes 2 and 3, depending on the rules at the time).
So any kick that will hit the target is scored. But a punch has to have an actual effect. The punch has to knock the person back, knock them down, or visibly disrupt them enough to warrant a point. So while, in general, I can play tag with my feet and score tons of points, if I want to use a punch, I have to make it count, or it doesn't count.
Daedo System
Using the electronic scoring system, there are sensors in the chestguard and headguard that record hits from more sensors on your instep and heel. (This is why ball-of-the-foot kicks aren't trained in KKW TKD). There are no sensors in your hands. I'm not sure if you can even score on a punch with Daedo, but if you do it is a judge's call, and not a sensor hit. So if you're making contact with your feet, it's up to the impartial sensor. If you make contact with your hands, it can be up to the judge, and again - it has to be a staggering blow.
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Now, this isn't to say that punches aren't useful. A good punch to the solar plexus can knock the wind out of a fighter. Punches are good distancing techniques to knock them out of ax kick range or to set up your own kicks. Punches are really useful against smaller fighters up close when you can't use your feet.
But when you can score 2-3 points per kick and kicks score more often than punches, they don't really get used. There's also that a staggering blow takes the opponent out of range of a follow-up punch, so you can't really combo points into punches. You can do roundhouse kick- double punch - roundhouse kick and get a few points from the kicks, but you can't string several punches together and get points on all of them.