It's not a matter of principle, it's a matter of headaches. It's very unlikely that a customer like that would pay enough to make it worthwhile.
However if the alternative is bankruptcy I think there IS money to be spent on the solution.
You know how employers are skeptical to hire people who start the interview by saying how awful their last/current workplace was/is? Same here. I've definitely met hundreds of developers or sysadmins that I wouldn't trust, and whose services I wouldn't recommend. I've definitely been wrong and hired some of them myself. But I would never say something like that in public. At the end of the day, who's the smartass that hired these people in the first place? I get it's frustrating but such is life, you still have to be professional about it.
Plus, 200 USD/hour for a quick fix looks like a great deal, but even if the fix itself takes one hour, it's rarely a one-hour job with customers like these. You routinely end up invoicing for less time than you spend deflecting their attempts to negotiate the bill, explaining why it took one hour and itemizing it, and getting them to pay the stupid invoice.
The sysadmin resigned, no tech person anymore. The boss got a lost password inquiry from a customer, panicked, called former admin for help, not a single word he understood, hit the forum.
And in the forum post he said the admin “wouldn’t cooperate”, “very adamant and confrontational” about “giving out encryption keys” to “decrypt valuable customer database we can’t afford to rebuild but might have to” and how it’s driving the company towards bankruptcy over last few days etc etc.
Eventually forum members realized he’s talking about a password reset, and convinced him it’s actually impossible to recover hashed password nor it’s necessary which is the point, you just verify identity and let them change the password etc etc, but it took hours for the community, on top of a day and half or so of tense hours for the boss guy’s company, to just understand the situation and act accordingly.
So I think it might be worth communicating how passwords work every once in a while.