(finally got around to answering)
OST has medkits on all their mainline infantry that can be used on any squad but that doesn't change that it can also have one of the most inexpensive healing bunker. OKW light vehicles aren't any better than T-70, Stuart or M20.
Sturmpioneers medkits used to be unlocked with veterancy, and passive healing for volksgrenadiers used to be unlocked way before than vet 5 so whatever the original design was it doesn't really matter. USF was designed to not have a tier 0 mortar
OST medkits function very differently though. No AoE healing, casting time and you can "only" use it on your main line. Medkit crates can be picked up by anyone and most importantly provide AoE healing, practically cutting the price at least in half. However you are fixed in place, but that is the case with any "medic squad" healing as well, which they are meant to replace.
It really doesn't
Claiming that it worked because Mechanized used to be meta ignores the fact that LVs are ALWAYS the meta for all factions, that the Battlegroup started seeing use because the flak ht was improved after being useless for a lot, as well as several key changes that OKW went through
Mechanized builds were nerfed, and so were Volksgrenadiers, which made Mechanized builds much less powerful. Ultimately there's no "meta" for OKW because the faction is competitively dead with 3 picks and 0% winrate in the last ML5, volksgreandiers late game bleed and inefficient trading being great part of it, which is only made worse by the lack of healing without backtech
OKW is strong in all modes (outside of tournaments), and even in 1v1 does not lack much behind Ostheer if at all. The lack of tournament play is something to be concerned about for sure, but given that larger stat samples show otherwise this does not seem to be a problem outside of the top 20 players.
Regarding LVs: OKW functioned well on T2 builds, even without a heavy to crutch on. Players still seemed to choose T2 builds despite the heavy mun bleed for a long time. Now their T1 got stronger and more accessible. Now there indeed is some powercreep that made other factions easier to play as well. Maybe my view on this is scewed, but I see both T1 and T2 builds regularly in the game.
The only faction in game that has a fully linear teching is Ostheer, because the mod team went out of their way to force a fully linear teching and disincentivize Tier 0 into Tier 2 builds, and still, OST can ignore the Tier 4 if not accessible. UKF has several side techs and Anvil + Hammer. No faction would be similar. Even OKW itself wouldn't change since its bad design basically always accounted for the player fully teching anyway, which works in resource inflated teamgames but gets absolutely stomped in 1vs1
It would still be a ridicolous munition sink. The only good med crate is the 221 because it can be dropped as single one to heal whenever you want field presence, which is a good tradeoff and a useful ability. Healing an entire match off sturmpios med crate *3 in your base costs simply too much and is far from what Relic probably originally designed med crates dropped by infantry for.
The aim of my suggestion is to slightly reduce the mun bleed of OKW from the mid game onwards. This should keep the intended trade off between STGs and healing intact while allowing more munitions float later on. As you said, OKW is supposed to get all trucks out at some point. If the resource pressure is too high in 1v1 but not in team games, SP veterancy might actually be the way to go. SPs shine in 1v1 situations and can level up quicker, while they are worse in team games. Additionally, wipes are also easier in team games due to more arty. This change should therefore benefit 1v1s more than team games and would ease the pressure of getting T1 out after teching T2 and T3.