Because it's not about the person, it's about the Dharma, the teachings. Those exist with or without a historical Buddha, and that's what guides the practice.

Imagine that someone is showing you the moon by pointing at it. You want to look at the moon, not the finger. The Buddha is a finger pointing at the moon.

Enlightenment isn't about some mystical truth and seeing into the unknown. It's about stripping away the illusions that cloud the way we see this reality. Those stories about the Buddha are ways to illustrate some of those illusions and how others might have come to the realization. It doesn't matter if they really happened. A lot of them are so constructed that they are probably fake, at least to some degree.

One that really affected me was the 72 problems story (or some number lol, I only remember that it's not 99, because 99 problems is from that Jay-z song, but ultimately it doesn't matter how many problems "everyone has").

For the short version, a man goes to the Buddha because he heard he can help him with his problems. He complains about his farm not doing well, his wife nagging, his kids not respecting him, a whole slew of 72 or so problems, and for each one when he asks if the Buddha can help him with that, the Buddha tells him no. Finally he complains that he didn't help him with any problem and the Buddha says "everyone has 72 problems, but I can help you with your 73rd problem: the problem that you have problems. Problems are a fact of life, if you get so bent up about having problems, you're going to have a miserable life because there's always problems. Accept that the problems exist and you'll find peace." And then the guy was enlightened (in that specific aspect of life, since enlightenment isn't a global state but basically just means "learned a deep lesson").

I'd get annoyed at needing to deal with things. Still do sometimes; enlightenment isn't some magical state. But when I notice that that is bugging me, I just remember the 72 problems story and dismiss that 73rd problem from affecting my mood. Which also indirectly helps with the problems themselves, because if you're pissed about having to deal with stuff, you'll be less effective at dealing with them (especially if your mood rubs off on others or attracts trolls). It truly feels like understanding that enabled an easy mode on some aspects of life. If the whole story was made up, it doesn't undo that understanding or eliminate that easy mode.

Whereas I've known Christians who can't understand why atheists don't just go around murdering people because if they don't believe in the Bible, what's even the point of trying to be good?

Because it doesn't change the message at all. And if you follow a religion because you agree with its teachings, does the source really matter??

If you read somewhere you should be kind to others for betterment of the society. You said "that makes sense, I'll do it from now onwards", and you later learn it was a fantasy story and wasn't talking about real life, would you stop being kind? Now replace that with not actively hurting people.

This is why Christianity is so scummy. The only reason these shit heels “give back” is because they expect to he rewarded for it. Oh no, we can’t just be kind to be kind, we do it because we are promised something on the back end. Same energy and douchebags who record themselves donating to say the homeless. It’s all about what they get out of the transaction. A fucking pat on the back.