I know for a fact this was suggested, very early on in the game's life in fact, and devs at the time said they'd be open to such a skill line but it never got implemented. We see NPCs using single one hand weapons, we have the High Elf Hero using a single one hand weapon and a spell, why not us?
Currently, equipping a single 1h weapon does nothing, it has no corresponding skill line, adding additional classes of equipment for the off-hand wouldn't even be necessary. Just equip a 1h weapon and get XP and you gain the skill line.
I know a challenge might be leveling the playing field with single weapon stats rather than DW or 2h, but I'd imagine passives could compensate.
Please let me be like our High Elf Hero!
I know I already commented here, but...
We've got this Golden Pursuit, Vengeance, and of course our Tamriel Tomes going on right now. I don't have time for all of these time-limited activities. Of these, I probably will be dropping Vengeance--even though I like Vengeance--because I like collecting emotes.
I'd have liked to play a little Vengeance, too, but I've only got so much time.