A lot of mayors did that. Truth be told, even New York City's mayor did that.
Problem is that it doesn't make a difference. Lots of other mayors will give the incentives. And, as in the case of NYC, sometimes the governors will come in and override the decision not to give subsidies anyway. (Although in the case of NYC it likely wouldn't have really mattered. I suspect they would have won the HQ2 subsidies or no subsidies.)
Lots of mayors will give the incentives? Fine. Let them. If you think it's a bad idea - or even a bad idea for your city - then don't give them. If someone else will make the mistake, let them make the mistake (and reap the consequences).