Warriors that are running DW right now avoid that massive miss chance by using a /stopcasting macro with Heroic Strike and a swing timer. When HS is queued, that extra 19%(IIRC) miss chance from dual wielding is negated on your off-hand - the game reads your off-hand auto-attack as a special attack while it’s queued, and this was confirmed to be “working as intended” four years ago (Ctrl+F “Heroic Strike”) - so you queue HS, let your off-hand hit, /stopcasting before the HS goes off with your main hand swing.
It’s still probably smoother to level with a 2h weapon(especially if you’re averse to swing timers and macros), but it doesn’t require a ton of hit gear. You do still get that extra 19% miss chance with your main hand weapon’s white hits, so if you aren’t doing considerable damage with your off-hand weapon, you’re not generating a lot of rage with it.