Third and fourth year are less about 'doing procedures' and more about learning to take better histories, perform thorough exams, improve your clinical decision making capacity, give concise oral presentations, and manage numerous patients on the service. And in the process... learning what we want to be when we grow up. Procedures tend to be a small part of the puzzle, and if your clinical rotations are at a hospital where residents are also trying (needing) to gain experience, the med students role in procedures is often limited. There are always exceptions to this, and it really depends on what experience you seek as a medical student. During fourth year, you can load up your schedule with rotatations where you'll get your hands a little more dirty -- anesthesia, surgery sub-I, any rotation in a rural setting, etc.
With that said, as a medical student, I did lumbar punctures, delivered 5 babies, first assisted on about 10 surgical procedures, placed 2 art lines, became handy with a speculum, intubated a handful of patients, sutured here and there, did a sonohysterogram and a colonoscopy (all with close supervision and help, of course). Enough to feel comfortable with each of these procedures? Heck no. But it helped me learn whether I was a procedural oriented person or not. Did I like scrubbing in and participating in OR cases or did I prefer rounding on patients for 5 hours straight? Each rotation is not really about teaching you how to 'be' that type of doctor. Our surgery director told us on the first day of our third year clerkship something along the lines of, 'I don't care if surgery bores your to tears and you never step foot in an OR again. But for 8 weeks you get to live like a surgeon, so suck it up, and when you are a phyician out there you'll understand what we do and when to refer patients to us.'
Hope this helps.