There are three really convincing arguments I've heard for this - I'm not sure which is "correct" and explains the FAA's logic, but personally I suspect it's a little bit of each.
Argument 1: Night landings are "special".
A night landing is definitely different from a day landing - there's much less of a sight picture in the flare unless your airport is in a really bright area or you have a bright moon (and even then it's "different").
If all you're doing is tapping your wheels on the ground and quickly accelerating back to takeoff speed you're missing a lot of what a landing is - bringing the nose down, decelerating to a safe taxi speed, and leaving the runway under control.
Which conveniently brings us to...
Argument 2: "You gotta learn how to taxi all over again!"
That's something my instructor told me, and I didn't really understand what he meant until I was in the plane. Airports are really dark and it's hard to find your way around the taxiways at night. Personally I think a big part of this requirement is the intent that you taxi off the runway and make your way back to the end to shoot another circuit. The hardest thing about my night training - aside from finding the darn airports was taxiing around without getting lost.
(Of course the regs don't say anything about "Taxi off the runway" - they just say "full stop". You can satisfy the legal requirement with "stop-and-go" landings, but there's a nagging voice in my head that says you're not really "getting current" if that's all you do...)
Argument 3: It slows your procedures down, which makes you safer.
Touch-and-Go landings are kinda dangerous if you think about them - Bring the plane in for a landing (which is already a lot of work). Now as soon as all your wheels are on the ground make a mental judgment as to whether you have enough runway to take off from given your current position & rolling start, if so retract your flaps to an appropriate takeoff setting, cram the throttle back in, and take off again..
When you look at them that way it's a bit odd that we have students do them (and there's more than one CFI around on the internet who says it's a lousy teaching tool).
Adding "Oh yeah, and it's dark out!" to that already difficult and dangerous procedure above is just begging for an accident - especially in a retractable gear aircraft (gear lever, flaps lever, and what happens if you miss in the dark cockpit?).