My opinion only, but if I had to bring an outside offer to get an inside raise, I'd take the offer. "We'll pay everyone what we can get away with, except the few who we need for the moment that make a stink." But then, I make too big a deal about personal relationships, and I forget that it's just bidness.
That said, I did get a raise once with an outside offer. But I left just inside a year later.
I agree and it can be personally very distressing when you know you are delivering tremendous value and are not getting nearly the financial reward for the value you bring.... and yet can't seem to convince the bosses to put up!
That's why I look at it now as a system that just needs the outside data point in order to properly process the request. It's not a person holding back the raise, more often the process which the outside offer fixes.
If there was such a thing as an "employee appraisal" service maybe you could do it without actually going to interview, which would be pretty cool!
That said, I did get a raise once with an outside offer. But I left just inside a year later.