"help an ally shrug off a condition" could mean flushing poison out of their system. You can't do that in a six second action, and if you could it would be a medicine check or something similar. And actually, if it is a poison that grants saves, you could use your action to give them an antitoxin to grant them advantage.
A lot of other conditions would be harder, like petrification. I guess if you wanted to use your action to grant them advantage on a fear save, by trying to get them to see it is an illusion that could work, but here's the problem. That is something anyone can do. The wizard could also take that exact same action, why should it be a special ability?
Now, in my personal remake of the Banneret, they actually have an ability similar to what you are talking about. It is a high level ability, but they get to use their reaction to let an ally remake a save, and if they are within the "banner aura" (a mechanic I made to represent the banneret wielding a flag of battle, which inspires their allies and makes all of their abilities stronger) then the reroll gets to add the Banneret's charisma to the roll. The Banner also gives bonuses to fear and charm saves equal to the same amount as long as you are holding it to allies within a certain distance (10/20/30 depending on level) and you can make a speech as an action to give your allies a more save bonuses and fear enemies.
However, this is all tied to the idea that the Fighter understands the power of banners in the battlefield. Now, maybe this fixes a bunch of issues for you, but this ties back to my original point. This class is the Banneret Fighter, not some new class, not some spell-less bard. It fits as a fighter
So, we don't need more non-magic classes, the fighter, rogue, barbarian and monk have the conceptual space they need to cover us. Maybe they need to have better designed subclasses, but the concepts are there.
I was thinking of Paladin auras, since they are the only auras usually in the game. And they are magical in my mind, the basic aura gives up to a +5 to the ability to dodge lightning, resist poison, rip free of vines, and resist mental attacks, at the same time. I fully agree that the there are incredibly skilled and inspiring leaders in real-life, but no matter how inspiring you are, you can't prevent someone from dying due to rattlesnake venom with your words alone in real life.
Now, this seems at odds with my Banneret, which does exactly this. I never called it out as magical (nothing is enchanted after all) but I run deeply magical worlds, where symbolism matters. The symbol of the banner and what it means to the people draws on something. It could easily be a very subtle magic. I don't make a judgement either way with it, but aura's as presented so far in 5e are all magical, and I think the designers intend to keep that going, because that would explain why being 15 ft away removes the bonus at low levels, when otherwise you can see and hear the source of the aura just fine. I mean, I can see someone 15 feet away pretty easily.
That all sounds amazing, but I think I've been unclear.
Does that up above really need a new class? Or just a new system for fighters or a new subclass? I could see that Enemy prediction ability being a feat or a rewrite of the Battlemasters "Know your enemy" feature.
One thing I forgot to mention from the first part of this post is that you scoffing at the Tool Proficiency isn't a problem with the fighter, it is a problem with the crafting system. I'm playing a rogue thief that fairly consistently throws alchemical items in combat, makes them himself, I had to find a 3pp supplement for crafting items though, because the crafting system is busted. But, fix that crafting system, and I don't think you need an "alchemist class" because everything they are doing is something that you should be able to do with the alchemist kit (I am also growing more and more convinced that alchemy and herbalism need to be combined, they overlap too much)
So, it sounds like the solution isn't "we need more non-magical classes" it sounds to me like we need more non-magical systems.
As someone who was in marching band, I get that. But, assuming the weather isn't boiling hot, I'd say that about an hour after the end of a short parade I could have done the parade again. I certainly could keep walking after, since we generally had to walk back from the end of the parade route back to where the pick-up area was.
But, take something like disarming an opponent. One of the big problems people had with 4e, and have with the battlemaster, is that you can't disarm an opponent every single round. Why not? I knocked the weapon out of his hand once, but now I forgot how to do it?
Look how the healer feat or Inspiring Leader feats are limited. You can do them infinitely, but the recipient can only benefit from them once per short rest. A healer doesn't forget how to heal after doing it six times, but the bodies of the people they have healed have already been treated as best as they can for now. An Inspiring Leader can give an hour long speech and inspire 60 individuals, but you can't inspire the same person over and over again without giving them a break to rest and renew that inner resource you are calling up.
So, if you added a bunch of 3/day abilities to the fighter or rogue, people are going to get upset. And, if you do things like give out feats that allow them to use their skills in "new ways" you run into the same problem we had with the Menacing feat, "now that it is a feat, I can't let my players use the intimidation skill to give someone the frightened condition, this should just be something you can do with the skill, not a feat"
But, alternatively, if you just make this type of stuff an artifact of the skill system, then it doesn't help fighters and barbarians who don't have a as much interaction with that system as the rogues and bards.
Don't misunderstand me, I'm not saying that people shouldn't try to make these systems and expand the game, but I am pointing out that it is a tricky needle to thread.
ROFLOL, I'm dying over here. That is such a perfect description of that moment.
Reaper: Dude, it has been hours, you literally have no blood left in your body, it is all poison.
Beowulf: Is the gold piled up to the ceiling?
Reaper: .... no
Beowulf: I ain't dying yet then.
I know it was most common in 4E, but I remember seeing "at-will" abilities and spells in 3.X as well. Was it just monsters who had that or were there a few late edition magic classes that had it too?