The professional adventurer thing is easy, and it works. I’ve had whole campaigns based around the professional explorer types. One rumor, a scrap of a map, and off they go. The thing is, professional adventurers aren’t the same thing as heroes, though the two needn’t be separate entities. Professional adventurers still have motivations, whether those be curiosity, lust for knowledge, greed, or some queer combination of those and more. Most of these characters also have desires and histories that provide hooks for other types of stories. There’s nothing wrong with that either.
I think the major problem that can arise is when the DM provides no guidance for persons who wish to create story-rich characters, and other types of players don’t co-create to make a group that works together. These two failings inevitably lead to impasses as the method actor cries, “Where’s my motivation?” and the others cry, “Just follow us—we three don’t have any reasons to even be together, much less go on the adventure.” Such problems also lead to situations in which the party has no reason to help each other, much less someone else in need.
If the situation were the opposite, the method actor might be able to say, “My character isn’t personally interested in this, but she’ll go to protect her friends.” That’s real enough. As is, “My character isn’t personally interested in this, but he’ll go to make sure something interesting doesn’t happen without him.” The list goes on. (“Those @%#$^@s aren’t going anywhere without me. They owe me, and I aim to collect!)
Even professional adventurers need reasons to work together, otherwise inter-party conflict is usually soon in the offing. Who would take a group of three unknown ruffians with him into the Temple of Abominable Awfulness? A fool, and that’s about it. People team up to compliment each other and ensure success, and the wise avoid as many unknowns as possible. There’ll be enough unknowns in the Temple.
Someone who has a character that can’t be hooked also has a character that would be boring in any other form of entertainment, from novels to films. That person has created an uninteresting situation by creating a lackluster character. If boredom follows, it’s not the DM’s fault.
Even kick-in-the-door players need loose back-stories to tie their characters to one another with some form of loyalty. Call it the Krusk-Vadania-Soveliss method of party construction. (Vadania or Soveliss can tie into Mialee, Devis, or even Nebbin for a little arcane power.) That is, unless there’s to be no roleplaying whatsoever. If it’s go in, pound the monster, and grab the loot, then that’s very much like a video game. It’s no wonder such players would prefer Diablo or some MMORPG, either. The gratification is quicker and easier.
I don’t think there’s any right way or wrong way to play. If you’re having fun, you’re doing it right. But you get out of the game as much as you put in.