That made me laugh a bit.. I have two full sized trucks today, both with V8 engines. One gets "almost" 14 mpg, the other is less than 12. I doubt the designers gave much thought to dropping the spare to improve mileage. I doubt it would help if I did remove the spare and associated tools. Maybe, but I doubt it.
It would help, from the auto maker's perspective, but not yours. Any mileage gain you'd see would be inconsequential. However, when dealing with Corporate Average Fuel Econony (CAFE) standards, they're looking to eke out any mpg improvement they can get, to boost the fleet averages up.
Nowadays I think there's some formula that takes the "footprint" of a vehicle into account, but in the old days, there were two standards: passenger cars and trucks. And what comprised a "truck" isn't what you might think. The Dodge Magnum (the wagon of the 2000's, not the "Adult Toy from Dodge" of '78-79 vintage) was actually classified as a truck! It has something to do with ascent/departure angles or something like that...basically if you have less front/rear overhang, you can approach steeper angles without scraping. And it has to have a flat load floor behind the front seat. Either with any back seats taken out, or folded flat.
Actually, I think there may have been four standards for awhile: Domestic cars, domestic trucks, and foreign cars and foreign trucks. I remember reading that Ford put just enough non-US/Canada content into their Crown Vic/Grand Marquis/Town Car in some later years, that they actually qualified as foreign cars!
But anyway, trucks have traditionally been held to a lower standard than passenger cars, so there was less incentive to jetison the extra weight.
Also, for those CAFE standards, they take the raw, unadjusted economy ratings of the vehicles, not what's on the window sticker. And those raw numbers are pretty generous. I remember my old Intrepid, which was rated 21/29, was something like 24/28 by the raw laboratory numbers. And, since then, they've adjusted the window sticker numbers down somewhat. Under the new metrics, which came into play around 2008 I think, my old Intrepid is rated around 18/27.