the old box has to be accessible -- you cannot make any cabling connection hidden or inaccessible so to the extent you are making connections in those desk-height boxes you have to put plates on them. This rule exists for very good reasons. If your connection hidden in the wall became loose or caused a short, you or the next homeowner would have no idea where it could be or where to look to fix it.
You can certainly get rid of the need for the boxes at desk height by rerouting the cable that leads to them. How much work that entails depends on how they are wired.