People like what they are used to seeing (the rook being smaller) but what you say makes sense. I woulden't like the rook to be bigger because I'm one of those that "likes what they are used to" but it's an idea that don't bother me it seems like good reasoning to me.
Why is the Rook shorter than the minor pieces?

I was wondering the same thing the other day, but I think I actually prefer the rook to be shorter, makes everything unrealistic and bizarre.

I always assumed it was so that you didn't knock over the rooks as you moved pieces. Being in the corner of the board you move your hand over the top of them quite a bit (when in the starting position) to move other pieces.
Maybe it is because it is the only piece (not pawns) not to have a proper "hat", K+Q have Crowns, B has the Pointy thing, and the Knight is the front part of the Pantomime horse.

I think the rook is shorter than the minor pieces to make the appearance of a chess set more pleasant overall. The gradual declining slope in both directions going from K and Q to the rooks makes a uniform and appealing "line". If the rooks were taller than the minor pieces this pleasant gradual declining slope would be shattered and I also dont think it looks good. I personally would not want a chess set in which the rooks are taller than the minor pieces.

For Staunton designs, it's the traditional aesthetic, though I've seen some rooks in HOS sets that are bigger than the minor pieces. Sometimes the rook may be shorter but pretty big around and as massive as either bishop or knight.
To my eyes, many classical designs are simply inspired even if they are just pieces of wood to someone else.
http://smg.photobucket.com/albums/v737/MooscaHumano/?action=view¤t=HOSCollectorcopy.jpg

I think the rook is shorter than the minor pieces to make the appearance of a chess set more pleasant overall. The gradual declining slope in both directions going from K and Q to the rooks makes a uniform and appealing "line". If the rooks were taller than the minor pieces this pleasant gradual declining slope would be shattered and I also dont think it looks good. I personally would not want a chess set in which the rooks are taller than the minor pieces.
This was my initial reaction as well -- I think it's likely just an asthetic preference.
Now, why are dimes smaller than nickles...?
I'm in the market for a tournament wooden chess set and I stumbled across the Renegade Series. It's too expensive for me to risk in tournament play but what's interesting is that the rook is bigger than the minor pieces. The typical value of the pieces is identifiable by size. Most chess sets don't have a relation between size and value of pieces so I was a bit surprised by this idea. However, it seems to make a lot of sense. Moreover, Rooks are sometimes called castles or towers so it would follow that they should be tall. What do you guys think about this and which way would you prefer it?