I think the idea is, when players don't yet know any of the rules, starting in a tavern is a rules-light place. Conflict is possible, but unlikely, you don't want to piss off your main source of booze and jobs, after all. Opportunities seem highly plausible: taverns can have anybody in them, there's the (perhaps literary-driven) perception that a smoky late-night tavern could have just about anybody, and some of those people might be someone looking to hire some muscle. Finally, it creates golden opportunities for players to ask questions about the world around them, since various tavern-goers naturally invite such things, the publican/bartender/innkeep/etc. is likely to be an ongoing minor NPC and thus worth getting to know, and someone can ingratiate themselves with the party (or the party can ingratiate themselves with others, if they have a bit of cash) by simply offering a round of free drinks.
This also creates a situation where the GM can narrate without narration--by speaking the words through an NPC's mouth. Instead of simply narrating what the exterior of the dungeon looks like, the GM can have the prospective-employer NPC describe what they know of the place. It becomes a dialogue, with opportunities for the players to display their investment into the world (whether that be roleplay in terms of acting and voicing, or roleplay in terms of smart questions, good planning, or canny foresight). Plus, by being a dialogue, despite being a lower-stakes environment, it actually can be more interactive than an abrupt "you appear in front of the dungeon" situation.
And that last bit might be the biggest reason why this sticks around. A tavern start where the party decides to take a job manages to be more interactive and a gentler introduction at the same time--a rare combination.