First off your flight is probably not all the way full. There may be no seats shown as available, but that may be because all of the advance purchase discount seats are sold out. You probably will be able to find seats on the flight if you look hard or select the unrestricted option.
As for switching equipment on US flights, it is very difficult. Airlines don't have that much flexibility to swap planes if one flight is full. Sure that 767 might be useful on one segment over a 757, but look at all the flights down the line that might be the other way around. It is just not that easy. Airlines try to get it down and not swap planes back and forth. There are many factors including numbers of first class seats and numbers of crew required that makes rescheduling planes difficult. It happens, but not often with in the United States among legacy carriers like DL
However that is not to say that it never happens. Certain carriers operate fleets of planes within a family. A good example is BA
. They operate 733s, 734s and 735s. It can be rather routine to get these planes moved around as to which is flying on which routes depending on capacity. These are all hub and spoke routes from London, but with BA
you don't really know what type of 737 you will be on as they will adjust according to load factors. However switching between a A319 and 737 is far less likely since commonality is an issue and you would need an entirely different flight crew in addition to other things.
If you have never designed an airplane part before, let the real designers do the work!