A wizard can spend one feat and not have to worry about Dex or mage armor ever again? No, that's too much.
A rogue wants to pick up a thematic weapon (or to use that Oathbow they just found) and needs to learn two other completely unused choices? That's too little, back to the original trap feats.
I don't have a good suggestion, but feats are supposed to balance ASIs. Taking one feat for medium armor and shield and +1 to Dex will grant you a lot more AC than +2 to Dex from an ASI.
Part of me wants to move proficiency training to the same downtime activity as tool training. Of course, I think that's a crazy amount of downtime for some campaigns but that's a different story.
The problem is that just one level of fighter gives you more than all these four feats.
And even if you don't use multiclassing, or if you feel delaying your spells by even one level is unacceptable, you can still fix this much cheaper than the RAW feats: just play a Mountain Dwarf!
You see my point?
I can't have feats that exist in isolation. I understand that the design process of D&D has been iterative. I can easily see how the game first created one choice (a feat, say) that on some level seems like a fair deal, but then independently offered a second choice (a race, say) that also, on some level, seems like a fair deal -
without drawing enough conclusions from this.
All I'm doing is recognizing that the proficiency feats are crazily expensive compared to other options.
Now, had those other options been deemed overpowered or unbalancing, it would have been a different story. But they aren't. I consider the multiclassing rules to be generally a success. Nobody thinks the Mountain Dwarf is the only choice for a Wizard.
Therefore I conclude the cost of an armor proficiency is vastly inflated by the feat. I conclude it is the feats that are expensive rather than the other way round.
My Martial Training feat might be radical, but I don't see how a powergamer will ever pick up proficiencies through a feat otherwise.
Had I thought two feats were more in line with multiclassing or choosing the "wrong race", I would have designed my feat(s) that way, but I don't. My hunch is that if the Wizard must pay more than one feat he'll simply take a level of fighter or dwarf instead.
So, before we discuss whether "just one feat to never have to worry about dex and mage armor ever again" is too good, we must first consider the alternatives. We must first discuss: how many feats do you think a player (conscious of making an effective build) will take before she starts to look at other options?
I realistically don't see any answer larger than one. How about you? Would you ever take more than one feat to gain armor proficiencies?
Now: what you could answer is: okay so two feats is too expensive, but one is still too cheap.
In other words, it would be fine for us to agree powergamers get their proficiencies from other sources than the feat subsystem
But now I've talked so much I'll leave that for later...
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Your Oathbow example: I don't have a good answer for you. Feats are certainly far too "big chunks" for one to be a good way to pick up something as small as a single weapon proficiency. I'm afraid D&D isn't really the game for "precision tweaks" like that.
I know - I have played many fantasy rpgs that are skill based (such as Basic Role-Playing). That level of granularity (a single skill, a single proficiency) is probably best handled by a background in 5th edition.
So, actually I do have a good answer for you

Design a background around the concept of getting a single weapon proficiency!