I'd definitely say that lockbashing should be in the game, it's nothing new, a number of other games allow this, and it kind of annoys me that the Elder Scrolls doesn't, because without it, players are basically forced to pick locks or use magic regardless of whether it fits their character to do so, because otherwise, they miss out on some loot, often some very good loot. Opening locks isn't something only thieves need to do, fighters do as well since some good items can be found in chests and dungeons, and most players aren't going to intentionally limit themselves by not getting that loot for the sake of role-playing, nor should they need to. The best RPG mechanics should be ones that actively encourage role-playing, at the very least, they shouldn't discourage it, Morrowind and Oblivion often required intentionally limiting yourself if you wanted to role-play, but my hope is that Skyrim can avoid this, and to do so, giving fighters a way to open locks is important. If this were a party based game, it might not be needed because you could have a thief in your party for those pesky locks, but in a game where you might choose not to travel with companions (And indeed, we don't even know if the companions in the game will be able to do things like pick locks even if you choose to travel with them.) it doesn't seem fair to count out fighters from opening locks when mages can do it.
Of course, bashing locks should have its limitations, whether or not you succeed with bashing a lock should depend on the weapon you use and how skilled you are with it, as well as of course the lock's strength, someone who has never held a weapon in his life should not be able to break open one of the best locks in the game with a dagger, and bashing locks should be noisy, not a problem if you don't plan on sneaking anyway, but it should discourage thieves from just bashing locks rather than doing it the way they're supposed to, if you want to give it another disadvantage, you could make it so there's some risk of damaging or breaking the contents of a container. And to keep things simple and balanced, I'd just have how strong a lock is for bashing determined by it's difficulty. Finally, to ensure it works with loading doors, locked doors or containers that have been bashed shouldn't actually be destroyed, they should just be unlocked, maybe with changes to their model reflecting that the lock is broken if you want to make things more detailed.
Another issue: the traps.
How handle a fire trap which can work both way: On the offender" but due to a sudden crash can also damage whats inside.
First, a more important question is "Are there trapped containers in Skyrim at all?" Because if trapped containers aren't even in the game, how they work is not a relevent question.
But if we assume the answer is yes, then I'd say it should be possible that the trap will be broken alone with the lock and rendered useless, or there could also be a chance that it will activate and effect you, perhaps depending on your skill, or simply upon chance.