actually... dagger + shield works great. i found it quite strong as i tried it on my sword'n'board warrior.
but running around in heavy armor, but attacking with an dagger felt weird to me.
Right, sure it works, but a sword be more effective. Daggers have no advantage over swords in the open - aside from tertiary advantages (like less stamina to power attack) (faster swing time- but really short reach). If you choose not to invest in any one-hand damage enhancers for enchants, then yes daggers won't lose an advantage, but that is a conscious choice not to take an option.
Totally workable and an RP choice for sure.
So daggers are a kind of bastard-child amongst the weapons in Skyrim. It's too bad they didn't have their own skill tree, or at least another dagger-specific perk or two, to make them a viable option on their own- for more than just sneak attack kills. Would have been cool to be a high-level dagger specialist/assassin that could also do rapid dual-wielded dagger attacks that could take something down *after* the stealth was gone in a situation- at least against lightly-armored opponents. As it is, you have to swap out to other gear in the middle of combat when that happens. Ah well. Maybe a mod someday

Well they do, that is what assassin blade is. Assassins blade combined with invisibility or to a lesser extent shadow warrior is about the most powerful thing in the game, and can easily deal the most damage available (unless using exploits- and that is an exponential that no one can argue.) If they also had skill trees like the alternative axes/maces/swords, then they would have the strongest sneak, the fastest swing, and competing perks. It would leave much to be desired for anything else to compete. IMO.
An dual wield dagger character certainly can be viable in the open, but he is better served in the shadows with daggers, and with blades in the open.
Are you referring to a kind of DF-reduction method (ala FONV) where say a dagger would cut right through leather but do nothing against plate armor? I do wish that existed, but alas it does not. Damage is damage and there are no barriers to overcome this time around. I feel the game would have been better served to have that.