A "real nihilist" might kill themselves (hey, is anyone needs to hear this, don't kill yourself, and definitely don't kill yourself because of a thought experiment [1]), but most of the nihilists I've met have adjusted to their perspective and responded to it in a healthy way. (I'm not gunnuh engage in a Scotsman argument about whether that's disqualifying. But I'll grant there's an obvious survivorship bias there.)

It turns out that believing in meaning isn't always necessary.

[1] A friend mine put this very well once. We were talking about Meno, and Socrates' refusal to flee Athens, dying instead on the principle he'd entered into a sort of social contract (please excuse the ahistorical terminology) with Athens.

"I've never heard Socrates talk about the social contract before," my friend said.

"I refuse to die over a minor fucking principle."

Dying for a thought experiment isn't romantic. Being rational in all things is actually undesirable, because not everything functions under rational principles (or we wouldn't need the concept in the first place, it would just be the air we breathe).

In the same way that everyone can make a cryptosystem they themselves can't break, everyone can create a logical knot that they can't untie. It's a parlor trick, and not a reason to die.