Two points.
1. The taxpayers pay for his time whether he spends it on this woman or spends it waiting for his food. That is not bad or good it is just a fact so we are indifferent , economically, to what he does with his time.
2.It is not an emergency whether she wastes his time or mine, but his time is no more valuable than mine so if I can be expected to wait so can the cop in my opinion.
The point is that his time shouldn't have been wasted by this silly person.
She cost the taxpayers money for which they received nothing of value.
his time is no more valuable than mine
It is to you, because you are paying for his time.
If he waits, you are paying him to wait rather than to do something more constructive with your money.