I was about 200 over my carry weight, and had an idea, so I turned into the vampire lord form, and viola, able to run as much as you can.
(I'm saying this is a bug. But I don't mind if you don't fix it.)

Not really a bug. if you get on your horse while over your limit, you can then fast travle to any point on the map. its good for moving house form Solitude to Riften

You can't really move through towns freely as a vampire lord though so its not much of an exploit, it still has its limitations, I don't really think it needs to be fixed... its the same as the horse trick, you can't take your horse inside cities so your in for a slow walk to your house, these things are fine the way they are to me, I think its the way it should stay.

I'm guessing they did this because you armor is forcefully unequipped when you transform and if you got the perks to make them weightless then they will suddenly add weight when you transform and you could get yourself screwed if you where close to your carry limit before you transformed.

The werewolf form is known to add 1900 carry weight when turned into, I assume they did the same with the vampire lord. Though If you have him it's better to use arvak, as long your in the wilderness. The transformations are better if your in a dungeon when OE.