I think the batting and use is what makes the difference. I have seen pictures of very old hand quilted quilts (think welsh quilts) that are just as densely quilted as any of today's quilts. Although I can't attest to how soft they are, pictures I have seen shown them draped over things that make me think they are like you describe. Antique batting was not bonded or needle punched or any of the modern conveniences we have today. Some quilts just had carded wool in them as the batting which required encasing it in something else, like cheesecloth type fabrics. Others had hand carded cotton. The nature of these battings required dense quilting to avoid batting migration and bearding usually 2" or less apart. Now I do agree that quilting spaced at 2" is not dense but I really think batting makes more of a difference than density of quilting. As a longarm quilter I have quilted both very densely and openly and IMHO the batting makes all the difference in the drape.
I definitely agree that use and repeated launderings will greatly contribute to a soft and drapey and cuddly quilt. Think of blue jeans. They really don't get nice and soft and comfortable until they have been used and laundered a lot. So even today's modern cotton battings will make a quilt soft and cuddly once it has been loved on for a while. But to hasten the process I would look for unbonded cotton battings like Quilters Dream. QD batting is still needle punched.
Another option is to not use any batting and back your quilts with something like Minkee and you will definitely get the feel you are remembering.