I've always wondered where the landing gear idea came from. First time I even heard of a saucer landing on a planet was the TNG manual. The large rectangles are loading ports, TMP shows this several times, I think Spock even uses one to exit the ship in the spacewalk scene. The ones at 2:11 are the access ports
Edit: The largest four rectangles are landing gear by design. Nice detail but utterly pointless.
I believe the information about the primary hull landing gear comes from
The Making of Star Trek by Stephen Whitfield. The book included a lot of information that had been developed as background but was unlikely to be used on screen. The saucer was meant to act as a lifeboat in the event of the destruction of the engineering hull. The main idea was to survive in the saucer and send out distress calls. Planetary landings were a last resort and the primary hull engines would be incapable of achieving lift off from the surface again.
I would have to assume the Galaxy class saucer isn't equipped with landing gear because it's simply too large to be properly supported by them. The entire landing gear idea (and the design of them into the details of the Constitution saucer) was part of Roddenberry's "Believability above all." approach to
Star Trek. That's also probably why there was information developed concerning the ability to blow off the warp nacelles (an idea that was later developed in TNG as ejecting the warp core).