It's not a dichotomy. How about "I'm going to become an adventurer so I can go in this hole in the ground and get filthy rich"? How about "I'm going to save my city from Evil Lord Whatsisname"?
The proportion of characters who think to themselves "I'm going to become an adventurer so I can become equal to the world's greatest swordsman [get to 20th level]" ought to be quite small, because seeking power for the sake of power is a very metagamey goal. It's more likely to be a player goal than a PC goal.
As I said, my character may meet their initial goal and then need to reevaluate whether they will retire. It may start as "I want to be filthy rich" and then morph to "If I don't defeat Count SuckYourBlood, I will never feel safe enough to spend all my phat lootz".
Or they may just decide to keep living the adventurer life because they're addicted to the excitement.
What I wouldn't personally want is to have a character that has such pathetic stats that I can't envision them as being a hero. Hence my preference for point buy over rolling dice. YMMV of course since there is no "one true way" to play the game.