In Oblivion, no matter how many times you whacked at one you would never level up (unless it was destruction of course). So, should training dummies count as enemies with unlimited health, that level you up, albeit at a slower rate?
1. Destruction only leveled you when it did damage on an enemy, or on you.
2. It would be nice, and would make them actually make sense for once. But it would have to be incredibly limited so it isn't abused. Same as using trainers, there have to be limitations. So, yeah, I think it'd be a small, but great improvement.
It did always make me laugh to see the guy in the Bloodworks of the Arena shooting arrows at a target, and thinking "Wow, that guy's wasting his time". Because targets, dummies, etc. certainly didn't do jack in Oblivion for anyone.
The exception being the "training partner" you got for the Fighter's Stronghold DLC. That was an attempt at reconciling the obvious fault in the weapon training, at least.