Two-Handed also works well with Heavy armor, provided you build for heavy burst damage. To that end you'd want an axe or hammer instead of a sword, since the build is meant to end fights quickly and those weapons do the most damage per individual strike.
As for mages: two-handed does not 'fail' against them, save through user error

. You will need to stack magic resistance, though, since you won't have a perked shield to absorb the shots with. Restoration can actually be rather helpful here, since you can dual-cast a healing spell while closing the gap; with the Respite perk you can heal back Stamina as well, which means you can sprint while doing so and still be able to power attack once in range. Alchemy does have the advantage of not putting away your weapon, but unless you hot-key potions you'll have to pause to use it, and some folks hate doing that as it breaks the flow of combat.
The Sweep perk is invaluable when fighting swarming foes, such as Falmer, Forsworn, or Bandits, as it lets you kill up to 6 at once with proper placement. Even if it doesn't kill them it does knock them down, which gives you time to heal. Warmaster is a good perk, but gets a bad rap; it only works with backwards power attacks, which can be difficult to land, so a lot of folks write it off without seeing what it can do.
Overall, though, 2H is still inferior to 1H+Shield, since the OP left-side Block perks don't work with weapons. You also lose up to two enchantment slots, but that's not necessarily a problem given that shields have rather limited enchantment options to begin with. Without a shield it's arguable which is better, although the higher strike rate of most 1H weapons means they can land more debilitating enchantments in the same time period, which is invaluable for those wearing Light Armor and not heavily investing in Smithing.
Dual-Wielding blows both of them away once perked-up; although you're completely open to incoming attacks since you cannot block at all, you often don't
need to block since they die before they can hit you. Casters are a headache unless you have really high magic resistance, but then almost all DW users invest in that because passive protections are all they have.