why do provider's ask if you are a local?  is being a local better or a deterrent?

Neither.  It simply leads the provider down a different path of screening questions and techniques.

None of which are likely to be revealed here, for their protection....

The 'correct' answer to that question ("are you local?") is the truth.

Some ladies, particularly in small communities, will not see local gentlemen, only travelers.

I imagine different ladies ask for different reasons.  Just be honest.

A local can more easily be a stalker, but can also more easily be a regular customer.  A locals wife is also a local, as are his co-worker.

Each lady has her own set of criteria for good and bad.  As the others have said, you are what you are.  I've found that telling ladies the truth helps make for the best experience.

OR suggestions on places to stay, etc.  This didn't seem to occur to anyone.
I do not ask if they're "local," however, i'll ask if they're nearby, from here [my city/state], from out-of-town, etc.  MOST of the time, if courteous, they'll flat out say at the beginning, "hello, i'm john smith, age xx, from timbukthree" OR "also in yourtown" and i got your email from ..., etc.
unless they've a bad local rep, they may simply be making conversation OR as i stated, wishing to know if you'd need directions, suggestions on airlines/motel/restaurants, etc. if from out-of-town; in other words, a benign question (to ME it is).