I'm based at an airfield with procedures, but no radar, and no controlled airspace. It never ceases to amaze me to see half a dozen TCAS contacts flying through the published FAT, not talking to the ATC unit controlling the airfield. A couple of times I've asked to delay the procedure until those contacts have passed.
Back to the point of the thread, depending on the direction you are approaching the airfield from it is often just as quick to fly the procedure as it is to accept vectors, and ATC are well aware of that.