Even if the setting is that of a game, the people who play it are still real people. If Kirito had gone through with Leafa's suggestion, she would have been hurt, even if it was her own idea.
And again, try to see things from Kirito's perspective. He's been awake for 2 months already, and Asuna has been asleep the entire time. Her family is marrying her off because quite frankly, the implication is that she'll never wake up. There's no "hope" of someone beating the game to keep them going. No victory condition.
Kirito breaks down, and Suguha tells him to stay strong and keep going. He gets a vague, blurry hope to cling to, and decides to check it out. From a realistic standpoint, the idea that Asuna is being held captive by Captain McRapeypants along with a bunch of other people for mind control research is quite frankly, completely ludicrous and unimaginable. If it wasn't a work of fiction, it's far more likely the only thing Kirito would find there is
nothing.
So why hurry?
(And if you think this self doubt should've been shown more, well, you're probably right, but it's important to remember most of the ALO stuff is being told from Leafa's perspective, not Kirito's. We get to see him as "Mysterious Brooding Stranger with a dark secret" instead.)
On that note