So what stops you as DM from removing the ability from fighters and house ruling something else (or nothing) in its place?
When I DM? Nothing, I already have a set of houserules of my own for the playtests. When I am a player, which is for the most part, I don't want to have to convince a DM each time of the reasoning behind my houserules. I don't always succeed in my attempts at convincing, but I usually do because my friends respect me and my judgment and vice versa.
For example, tonight my character turned level 4. We found a magic battle axe in a mound. I picked it up. Since I play a dual wielding ranger, I can't use it and my fighting style at the same time, or synergize with my class features effectively. But it sure was a nice axe. So upon turning to level 4, I looked at the Dual Wielder feat. Why exactly is it unbalanced to take one feat to be able to wield two non-light weapons again, exactly? It isn't. Not compared to Great Weapon Master or Polearm Master. I took the feat then asked my DM if I could forego the AC bonus to be able to dual wield regular sized weapons. My reasoning was that it was less than the +1 to hit and damage that boosting my strength would give, and that giving up the point of AC for the versatility of using non-light weapons, which are the most common magic weapon drops in the loot tables, is more than a balanced tradeoff. (Probably too harsh, actually, but I'm happy with it).
But the designers should have realized this would happen at tables all across the world playing their new game with a fetish for asymmetry (one non-light and one light weapon, that's for amateurs, not "Dual Wielders"). Instead, 5th edition is the first edition ever in which one can't dual wield battle axes or longswords, even with their "super feats" which are supposed to be a one stop shop for getting everything related to that in one go. Instead, the feat provides proficiency with all light weapons (whoop), a +1 to AC (didn't want that), and only one non-light weapon, so it's only half of what the feat should be doing, and doesn't even match the wording of the feat, which has the term "dual" in it. This is more like "crab style" feat, that would be a more appropriate name for it. That's a failure of design on their part that needlessly restricts common and valid character build choices so that one can't easily migrate over your characters from a prior edition in which this was legal (unless you use a houserule, which is not an elegant solution). I'd rather not have to waste my mental energy to correct shortcomings in the rules myself, and would have preferred that the actual designers understood that dual wielding such weapons was popular enough an option to support it in the official rules. This is all not to mention that their design "fix" for Drizzt clones is to make scimitars light weapons while rapiers aren't, which is just wrong in so many ways since scimitars are way heavier and harder to swing than rapiers. Now scimitars are just refluffed short swords. Why not make Drizzt clones take a feat? Also why full mod to main hand attacks and 0 mod to off hand attacks? More asymmetric design here, it rubs me the wrong way.
Incidentally, the very same designers made a very similar gaff in 4th edition. They made the Two-Weapon Fighting feat give only a +1 to the main hand attack, which made all your Twin Strikes lopsided and they errataed it a few years later because it was silly feat anyway and nobody was taking it because of the weird math and piddly bonus it gave. Now they are repeating their mistakes in certain ways, and this will also probably be errataed because I don't see them releasing a new feat to allow proper dual wielding in a later splat book just to correct this shortcoming in the new edition. I consider if fairly inevitable, I would just rather not have to deal with the headache of these kinds of "but doing d8 instead of d6 for one of your three attacks is so overpowered and we can't allow that. Meanwhile, double your damage feat for barbarians over here! Grab it while it's hot".
There are other issues with Second Wind than just the fact that it's a pseudo-lay on hands by a different name. It's by choice. Have you ever gone for a run and chosen to get your second wind? It's not a voluntary thing, it just kicks in at a certain point and I find the entire concept of the new fighter self-heal ability to be a highly amateurish, confused affair of contradictory mechanics that don't match their in-game effect.
Kamikaze, how can a first level fighter just take a whack in the head and shrug it off and say, I am just that tough? The barbarian does that with his rage ability via Temp HP. It's right there. It's stuff like that that makes me think the designers are all over the map and there's probably some tug of war between the designers going on behind the scenes. It feels like a design by committee in some places, where the manager isn't really doing his job to make sure all the pieces fit together well.
