So taking aside all the extra 'attack action' options you've got.....I'm a little confused with the intention here.
The intention is to open up the choice of weapons more to the "Rule of Cool". Why should every Barbarian need to use a Great Axe in order to be "optimized". I like seeing one Barbarian with a Great Axe, another with a Battle Axe and Dagger, and maybe another with a Broad Sword and Shield. Each of those options should be relatively equally effective, with differences in tactical choices rather than just a difference in damage.
Look at how many different weapons or combos Conan has used, and each option was equally effective in Conan's hands due to his training. In 5e a Wizard with 20 Strength hits just as easily and just as hard as a Barbarian using the same weapon. That does not feel right to me.
Another possibility with this approach is that Feats or Weapon Styles can be used to add advanced maneuvers or tactics to give more options instead of just flat bonuses.