It seems to me that fully threaded screws are commonly used to join wood, but I cannot see how any clamping force can be attained. Surely screws with some plain shank should be used so that the thread is only effective in one of the pieces. Am I just old-fashioned?
You can do two things to workaround the issue that comes up using fully threaded screws (that it is difficult to fully clamp the pieces together and they can potentially be pushed apart):
Clamp the pieces before screwing - this will ensure they are held tightly together.
Drill a larger pilot hole in the top piece. This prevents the screw from threading in the top piece and ends up working the same way that screws with a plain shank near the top work.
You're right to be concerned about the proliferation of modern "wood screws" that are fully-threaded as the design of traditional wood screws was quite deliberate to provide holding power into the piece of wood beneath without gripping the piece of wood on top (leading to a problem called bridging, where the screw's grip on both pieces doesn't allow any gap to close up).
However, you can still make use of them in the normal manner by drilling appropriate holes in each piece just as was done traditionally.
See previous Answer that covers clearance holes and pilot holes: Are there specific types of screws I should use for woodworking?
I find that when bridging happens, pushing the boards apart instead of drawing them together, I'll back the screw out, pull them together (by hand or with a clamp, as appropriate), then drive the screw home again. In almost every situation I've come across, this is sufficient to get the boards tight together.
I would agree, however, that an unthreaded portion of the screw or a clearance hole would eliminate the problem from the get go.