i have a battleaxe character, she was probably my favorite so far.
Almost all of my characters use 2-Handed swords. In Skyrim I've only played two that didn't: a dual-wielding assassin and a mage who did not use physical weapons at all. The rest were all greatsword users.
It was the same in the previous games too. I'd guess that well over 90% of the characters I've made in all the Elder Scrolls games have used only 2-handed swords.
None of my Elder Scrolls characters have ever used a shield. In my games shields are vendor trash.
I prefer two-handed weapons. Spears or greatswords. Currently my favorite sword in Skyrim is Knight's Greatsword from Jaysus Swords mod.
The gods gave you two hands, and you use them both for your weapon.. I can respect that.