Around here the pick and pulls charge a cover charge of a couple bucks and most search your toolbox on the way out. Still worth it but you have to be a little more careful with the free bits.
There are many more "auto salvage" yards where they pull the parts for you. Ahead of time. And you pay a LOT MORE for that, even if you didn't want it. Usually they won't let you on the yard and there's no chance you'll get that odd little widget even if you can see the carcass from the parking lot.
Years ago I frequented a yard that was old school - go ramble the muddy clay hills and see if you can find what you want. If you find it you could negotiate a price based on you pulling it or them pulling it. Had all kinds of cars back to the thirties. I went there after moving back here after several years and the yard had been completely cleaned out and sold for scrap. I was heartbroken.