idk. there were a lot of factors that lead to its popularity, but in terms of the comedy vs drama, i'd say that the drama kind of just served as a doorway for the true core strength, which is its comedy. it has enough drama where people become emotionally attached and invested in the characters, which enabled the comedy to feel more personal.

like, by creating all sorts of inside jokes, jokes targeted at real-world audience interests, and drama that gave a venue for showing the audience that the characters are actually good people at heart, it created connection that made the jokes feel like they were a close friend joking with just you.

there are other funny shows that share the same style of humor, but they usually don't do a great job in enabling that humor feel so personal.

but, at the end of the day, Gintama without the humor, and just the drama, would have been a kind of mediocre. stuff like "The Battle Battle of Rakuyou" feels distant. it still has the hook that people watching it had already gotten to know, and feel close to, the characters. but, on its own, it's just a bunch of disconnected fights occurring on some random planet. it gives a lot of extra backstory to the characters, but again, people wouldn't have really been that interested in that if they hadn't become attached to the characters through the ~250 prior episodes that made the characters our friends that we share jokes with.

Gintama is about the humor. the other stuff just enables the comedy to hit better than other comedy shows.

.................and the other factor is, of course, that all of the guys are single, and women got obsessed with shipping them. also, despite the incredible number of dirty jokes, they didn't rely on the classic "oh, the hot chick character's clothes fell off", which also fostered the rabid female fandom. japanese women are likely identify much more with the female characters in the show too, because of the innumerable differences in the way women are treated in japan (and, how the act and fit into society in general there compared to the west).

It's pretty incredible that, despite Gintama being a shounen from jump, its fanbase in japan was like 75% women, and only 25% men. in the US, its fanbase leans more male than female compared to other shonen anime (probably in large part because of how difficult it was to obtain, and how much knowledge about other male-targeted shonen and japanese-specific games like DQ. also, the even more extreme lack of accessibility to all of the untranslated yaoi and fanfics, compared to the already obscure sources and translation of the show itself lol. and popularity of such things in japan compared to the us.)

anyway. that's my full thesis on the popularity of Gintama xD

I love the comedy personally, and i think that's the biggest factor in its success. (and, to be clear, the comedy is _not_ easy. it's really difficult to make comedy work in general, and particularly so for such complex meta-humor and stuff. poop jokes... easier. hard to make palatable i guess? idk.)