We have Crawford himself telling us that this is not true.
I don't think Crawford said what you claimed.
You claimed
"short rests get dropped faster than combats get dropped." and
"that most groups do 4-5 combats per long rest"
Crawford did say Warlocks need to cast more spells and they don't get enough short rests, but that is because the number of combats is low.
Look at the WOTC published adventures: OOTA, TOA, ROFM, SKT, POA ....
Most days in these you are going to have 1 combat or 0 combats. With 1 combat that means Warlocks have less resources than other casters who can Nova and with 1 combat (or 0 combats) it is unlikely you do any actual short rests mechanically and even if you do short rests as a story element, without another encounter they are mechanically irrelevant.
I don't think Crawford said anything to support the idea that short rests get dropped faster than combats get dropped and even if he did, that certainly is not true on any large campaign published by WOTC with the possible exception of DOMM.
There are precious few adventuring days in published campaigns where you do 4-5 combats at all. You have a few, and in those few you are getting short rests IME.
Classes based on short rests are not getting enough short rests compared to how many long rests groups take. That is a fact, told to us by the very makers themselves. If you wish to dispute it with them, more power to you.
Not enough compared to the long rests they get sure, but that is not the same as saying they are not getting enough compared to the number of combats groups have and I don't think the makers themselves have said anything to indicate that is the case.
Nope! That is also emphatically untrue.
It is true. As I said dodging, even as an action, is rather often an optimal tactic.
Uh...no. Rogues are the bottom of the barrel. Try again.
Considering all 3 pillars of the game Rogues are substantially better than Barbarians at every single level, assuming Standard Array or Point Buy. At some levels Barbarians are better at the combat pillar alone but they are never the equal of a Rogue in the other two pillars.
The good Rogue subclasses also bring a lot more to the class than the Barbarian subclasses generally bring to the Barbarian.
Again, you conflate what I am speaking about with "optimization." I am not. Do not mistake caring about being effective with desiring to be the absolute most optimal possible thing.
What is the definition of effective then. This is a very gray area, at what point do you get so far away from optimal that you are not effective?
My arguement is a Monk is an effective character, not the most effective, but certainly effective and any class can be effective.
If a player is choosing to play, for example, a "Warlord-like" character (since you can't actually make a proper Warlord in 5e), they want that to be the thing they do best.
I don't agree with this. If I want to play a spell caster I can play a Wizard and be the best spell caster possible. I can play a Sorc or Cleric and be a pretty darn good spell caster but not as good as an optimal Wizard. I can play a Ranger and optimize my character for using spells and be a good controller and spell caster and while I won't be "the best at that" it will be what "I am best at".
That is not the thing Fighters to best.
What fighters do best is decided by how you build them. 5E is very flexible. Different people want different things out of a Warlord, but given the options currently available I would offer that a Ranger, Rogue or Cleric is probably the best Chassis for a "Warlord Like" character but you would have to build towards that and give up much of the archetype those classes are built around.
It does not matter what subclass you pick. Supporting other people is not, and in 5e-as-it-exists cannot be, the thing a Fighter is best at. Period.
I would disagree with this. The fighter is not the best class to build for this, but you can make a fighter that is best at this.
If you want to support other people - be a Halfling, take Battlemaster, superior technique, Bountiful Luck, martial adept, Gift of the Metallic Dragon, Magic Initiate-Cleric-Guidance-Resistance-Heroism, Fey Touched-Bless. Carry no weapons, when you are not using Battlemaster dice take the help action for your action.
This character will be best at supporting other people
Either you have to nerf their actual Fighter abilities into the ground
Yes exactly. I mentioned Rangers as controller above, I have actually played that into high level and I did exactly what you you claimed - I nerfed their martial abilities with weapons "into the ground". Yeah they still had extra attack, but they were not good using a Rapier with a 14 Dex and 8 Strength at level 14.
How is it not what you said? You're talking about building a character that supports, but does so by intentionally dumping all the things they're personally good at instead.
It is not what I said. I explained what I said. Building a fighter to be a helper in combat is not intentionally building a bad character. Building a fighter to be a helper in combat and then expecting him to function instead as a fighter, while swinging a greatsword with a 14 strength is what I said.
That's literally the same thing. You're dumping what you're actually good for doing, and replacing it with something clearly, demonstrably inferior.
Inferior is not the same as bad. Yes your helper fighter will be inferior to other helpers, but they won't be bad at that. They will be bad at the archetype abilities of a fighter.
I want a Warlord that doesn't have to dump anything. A Warlord where the thing it is already best at doing is supporting others. Where trying to do all the work yourself IS the "do something clearly, demonstrably inferior" option.
Ok. I don't have a problem with this. Helping others is not something I particularly enjoy and I don't think most players particularly enjoy this in a PC as compared to attacking or casting offensive spells or .... even doorway dodging.
I think this is a small number of players who like this, but I am not against a new class to cater to this desire. However don't denigrate the rest of us who do like playing Monks and do like using Patient Defense just because that is not something you want to do.