I find this a curious thing to say. Isn't this an argument against every possible remotely optimal computable form of induction or decision-making?

There might well be a theorem formalising that statement. There might also be one formalising the statement that every remotely optimal form of induction or decision-making is uncomputable. If that's the way it is, well, that's the way it is.

"Omega flies up to you

This is an argument of the form "Suppose X were true -- then X would be true! So couldn't X be true?"

"You start a business and discover one of your problems is NP-hard. You immediately declare bankruptcy because your optimal induction optimally infers that the problem cannot be solved and this most optimally limits your losses."

You try to find a method that solves enough examples of the NP-hard problem well enough to sell the solutions, such that your more bounded ambition puts you back in the realm of P. This is done all the time -- freight scheduling software, for example. Or airline ticket price searching. Part of designing optimising compilers is not attempting analyses that take insanely long.

And why NP-hard, exactly? You know there are a ton of harder complexity classes in the complexity zoo, right?

Harder classes are subsets of NP-hard, and everything in NP-hard is hard enough to make the point. Of course, there is the whole uncomputability zoo above all that, but computing the uncomputable is even more of a wild goose chase. "Omega flies up to you and hands you a box containing the Secrets of Immortality; for every digit of Chatin's Omega you correctly type in, you get an extra year, and it stops working after the first wrong answer".