Your particular suggestions need work.
You also need to watch out for other forms of multi-attack, like TWF, or crossbow expertise.
I didn't give all of my current ideas. I've been running the math on them. The barbarian and ranger end up getting buffs at 11th level and up. The paladin ends up getting a buff at 17 and up. Based the big damage comparison spreadsheet by [MENTION=6670944]Kryx[/MENTION], the other classes could use a bit of a buff; the Battlemaster Fighter is clearly on top of everything but two-Weapon fighting. But, I haven't seen them in play myself at those levels, and my goal isn't to "fix" that.
Here are my current ideas. Mathematically, the fighter compares well against the core fighter. The other classes compare well against the new fighter, but as I said they're buffed compared to their bases.
Barbarian: half damage on a miss with strength based melee attacks. This shows off the barbarian as a brutal attacker. Putting your shield and armor in the way doesn't block all of the damage; you still feel the force. Even a dodger has to overextend. In a 4E style approach, I'd do the "target Reflex defense" type thing, but attacks as save DCs isn't supported in 5th.
Justification: evoker wizard gets this with save based cantrips. Yeah, they don't get it on cantrip attacks. I suppose a floor could be used so sufficiently bad attacks (like if you have disadvantage?) can still miss for zero damage.
Valor Bard: give them war magic instead of Extra Attack. Also, add green flame blade and it's siblings to their cantrips.
Fighter: Weapon Mastery. At 5th, 11th, and 20th, they gain +1 to hit and +2 to damage. This makes them more accurate than the other warriors, even though their damage will end up slightly lower in certain cases.
Monk: I'm actually struggling here. Since they can use a weapon and are only forced unarmed for their martial arts and flurry attacks, I could just keep them as unarmed and change the unarmed scaling to Xd4. But, getting those extra modifiers on top of the extra weapon dice is tough. Also, without the unarmed die size scaling, monks will all hang onto quarterstaffs for ever (even though they already ideally hang onto them till 11th level when unarmed becomes 1d8). They only get 1 Extra Attack, so only one ability needs to be replaced. They could use a damage buff at higher levels.
Paladin: replace Extra Attack and improved divine smite with the +1d6 radiant damage at 5th and 11th.
Ranger: replace Extra Attack and their 11th level path feature with 1d6 sneak attack damage. I like what this will do to their playstyle as well. Reword their 11th level path features to be unique standard actions that don't stack.
Blade Warlock: remove their extra attack invocation and move their cha damage invocation to 6th level.
Bladesinger Wizard: War Magic at 6th level instead of Extra Attack.
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Starting at 5th level, you can split Attack. Split Attack allows you to reduce your damage by 1 weapon die to target two targets in range. Instead of 2[w]+ability to one target, you do 1[w]+ability to two targets. Yes, you do more combined to two than one, but that's to reward spreading (for the same reason that multitarget spells are supposed to do about 75% damage compared to single target spells).
Aside from the Rogue, base two weapon fighting is golden. Without the style, compare 1d6+ability and 1d6 short swords to 2d6+ability great sword. Identical, and they scale the same. TWFing costs a bonus action, but can split attacks earlier.
The style needs to be changed to allowing larger weapons. Then you get 2d6*+ability (8.33+ability) vs 1d8+ability +1d8 (9+ability). This partially shows how GWFing is weaker than Duelist (which needs to grant +2 damage to every die, otherwise it collapses). Then again, I'd rather change the fighting styles entirely anyway if given the chance.
For Rogue, I'd have to accept that a TWFing rogue gets a +3d6 damage boost for no reason. They don't need it. TWFing could be changed. As I said, I'm open to changing the styles entirely.
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