If you like casting spells, sure.
D&D is an imbalanced game. In 5e, "the martial/caster gap' is a notorious manifestation of that. In prior editions it was called "LFQW."
The martial/caster gap is not even real at all levels, it is only at certain levels and there are a bunch of assumptions and caveats that go into it.
There's a difference between optimal and viable. In a balanced game, a choice being arguably optimal (typically for a specific purpose) does not render other choices non-viable. In an imbalanced game it very easily can.
There are very, very few non-viable choices in 5E, but even those choices are not bad or wrong if someone wants to take them.
The designer deciding what genre of TTRPG he's going to create, and the GM deciding on the setting & themes of his campaign. The designer chooses what to include, and the GM what to ban.
This is exactly how WOTC did it! So pretty much it is as appropriate??
That's what balance does, maximizes the choices available to the player that are both meaningful and viable.
No it doesn't. As I noted most of the choices in the game right now are both viable and all of them are meaningful but they are not for the most part balanced (i.e. equal or nearly equal).
Whether another player in 4e thinks the Warlord's abilities are appropriate or not, a player who does find them appropriate could choose it, and play it without overshadowing other players or under-contributing to the success of the party.
And the exact same is true for a Champion fighter in 5E. As a matter of fact a Champion fighter in 5E can overshadow other players depending on a lot of variable and that could be either a good or bad thing depending on the table.
How? What do you mean "hurts the game?"
It equalizes choices so they are less meaningful in general. It doesn't matter what I choose the balance is the same.
I think it's clear to see how imbalanced choices, like trap options, hurt the game, both in the sense of making it a worse game, and in the sense of detracting from play experience. How does, for instance, making a former trap choice viable harm the game?
It is not clear at all.
Trap options yes, but there are very, very few of those and there are no trap classes in the game at all. I have no problem eliminating or buffing real trap options, but the martial classes, even Monk, are not that.
Of course, trying, and failing, to balance a game can make it even more imbalanced. For instance, over-compensating for a too-weak option could make it so OP that it renders multiple other options non-viable.
No it doesn't. If those options were viable before you overcompensated they are still viable after you overcompensated. Viable and equal are not the same thing.
Removing options instead of balancing them is partially self-defeating - there /will/ be less options
Exactly. So lets keep the underpowered options and the overpowered options and you have the choice of which you want.
For instance, in 5e, it would be fruitless to toss out full casters, even if it might make some martial choices more viable, because there are so many of them, the gain of a few newly-viable choices isn't worth the loss of many overall choices.
There would be no newly viable choices made by throwing out all casters. If a choice is not viable now, it won't be viable when you throw out casters either. Chainging one choice does not affect how viable another choice is.
You would need to change encounter or monster design or mechanics to make a choice that is currently not viable to be viable, and as noted earlier, there are very few non-viable choices in the game.
Conversely, removing martial options is a small decrease in overall choices, and just removes traps, the game isn't much improved, but it's being more honest with itself.
There are more trap choices for casters (specifically certain spells) than there are for martials.
As a matter of fact I can't think offhand of a single trap choice for martials. There probably are, but I just can't think of one right now.
There are plenty of spells like Withcbolt, Truestrike, find traps etc that are actually trap choices, there are also a few class-independant trap choices in feats but precious few.
You're free to believe that. There is absolutely no evidence it is the case.
There is absolutely no evidence it is not the case either.
I play a lot of D&D, with players from around the workd. I can only attest to what I have seen at tables I play on, but what I have seen does not support the theory that the game is less fun for most players due to the imbalance. There is actual evidence to support that.
Champion does relegate you to a more specific, less substantial role than EK or BM, which deliver similar DPR and geater versatility - and, both of which, in turn, fall short of what a full caster will open up for you.
No it doesn't because it is one of many choices you make and there is a level distinction in play here as well.
EK or RK does naturally enable more variety due to the mechanics, but that is different than saying it "relegates" you to more variety. Battlemaster offers a little bit more than Champion, but not a lot more and I would not call BM one of the better fighter subclasses.
Classes and subclass do not relegate you to much at all 5E. That is one of the great things about the game. Certain class/subclass options are better suited for certain play than others, but most are viable provided average or better ability rolls and choices made to suit your chosen role.
Using your example - I can take a champion designed as a wilderness survivalist and be very good at that. An EK, because of spells can be better. It has a higher ceiling. A Ranger can be better than either of those in that role. But all 3 of these can be viable in that role and you can make a Champion purposely built to fill that role that is viable. It is possible for a Champion built specifically for that to be better at it than a Ranger that is purposely built to lean away from that.
This is all about choice though, and if I want a wilderness survivalist who swings a Maul and crits on a 19, a Champion is probably the easiest single-class to do that with.