We still carry extra webbing with us for leaving behind but I've more or less stopped tieing my own runners as sewn ones are cheap and readily available. If the knot is good on the tied runner its NO different than a sewn sling except with a sewn one the connection point is generally cleaner than a knot and you are guaranteed that its good to the strength that the sling is rated, not to say a knot weakens the sling, but that you don't have to worry about checking your knots every outting.
As for slings over my shoulder, when I first started climbing back in the dark ages we carried almost all our slings over the shoulder, but now i climb with a mix of regular quickdraws and long runners doubled up like quickdraws on my harness. Unless a climb is known to need lots of long slings I don't usually throw any over the shoulder anymore.