If I were to send an illegal demand to someone (like say a threat of blackmail / extortion), can I simply "withdraw" the demand once it reaches court?
Absolutely ridiculous.
For the per se dispute, absolutely. That's what you went to court to get.
If your demand caused damages, that's a separate controversy that isn't cured by withdrawal.
Defendant: J/K!!!! lulz!!!!!
Judge: case dismissed! <bang>
It probably depends on how wealthy the defendant is (if an individual), or the size of the the org defendant represents. If you're a LEO type of org, then I'm honestly shocked the judge didn't just dismiss with prejudice from the off
The distinction is that blackmail and extortion are crimes. It's the act of sending them itself that is the crime, not the demand. If you withdraw it, it doesn't matter, because the crime already happened.
There's no criminal statute here. The NYPD asked for something. Someone challenged it as being "not something the NYPD is allowed to ask for". The NYPD said "never mind, you're right". That's the end of the story. If you want the law granting the NYPD the power to issue subpoenas to be withdrawn or modified, the solution is to elect representatives to do that for you. Courts are just the backstop for this process, and an imperfect one.
That said, if a law was passed to make "knowingly or recklessly false warrants" a crime, that might be one way to approach the issue.