Dragonball was a shonen anime that was action based but it was no way intended to be a comedy or "gag manga". Yeah, he obviously intended an element of humor with the names as it is ridiculous if a warrior planet has a bunch of vegetable named people, but at the same time, it's not all that uncommon to see odd object names as protagonist names in manga/anime. Dragonball just took it to an extreme.
For example, during the fight with Cell, when the news crew is still filming it during the early rounds, the different members of the news crew hear them hear them yelling "Gohan" and mention something along the lines of "I think they're talking about rice." This is one instance where it was made obvious they were making a joke (this part may have been filler, I'm not quite sure), but if the whole show was humor, why wouldn't outside characters like these make all sorts of these types of remarks and not wait until near the end of the show.
tl;dr: It was a joke put into the show, not an attempt to make the show a comedy sketch. Waiting for someone like Chou to intervene.
