2E could be low magic, it had the rules for it.
. 5E has to much magic baked into the core classes although I suppose you could cherry pick what classes a low magic setting would have.
Start with this:
Other than divine channeling, magic isn't really baked into those classes outside of spell casting.
At no point is any other class fundamental to the game or necessary. Remove any spells you don't want, probably cantrips and rituals (the basic game plays fine without them for closer to the becmi feel). Add classes, feats, and spells you might want from the PHB. Cutting and adding can be as little or as much as you deem appropriate. 5e low spell slots automatically becomes low magic without at-will magic.
Use the DMG dials for optional rules listed. Slow healing, healer kit dependency, rest variants, and lingering injuries changes the game up quite a bit. That's what I'm talking about when you mentioned a Game of Thrones style.
@Ashrym what @Zardnaar means with low magic is not that 2e is low magic per default, it is not. But it is very easy to tweak in the direction of low magic by e.g. limiting maximum spell level, or spell availability. Also it got more classes who either have no or a very limited casting ability.
If done nt proper it unbalances the already unbalanced 2e system even more, but people will not complain so much, because by commiting to play 2e (1e, basic) you are already committing to play an unbalanced system.
What I hated in 2e were the stat and saving throw and THAC0 tables, also the weapon having different dice for large mobs. You can easily reverse THACO and AC to match 5e but still you need a table to determine what THAC0 your char / a mob etc has (unless you remembered the rule +1 / level for fighter types +2/3 level for divine types etc...)
Skill system in 2e is also not very useful. Initiative in 2e if you use the weapon initiative is plainly wrong.
Spell durations, reaches, and AE are a PITA in 2e you gotta look everything up, everything scales etc.
Multiclassing level limits, stat boon and malus etc otoh are a thing I partially like. Establishing new races especially monstrous ones in 2e: much better than in 5e
I did play and master a lot of stuff in 2e as much than in 5e probably and I tend to say I know all its strengths and weaknesses, and without wanting to start edition war here: 5e is the best system for Tabletop D&D, because of things like bound accuracy and advantage disadvantage mechanic, fast combat, linearity, which make life so much easier for every type of player and DM.
I don't disagree with any of that. I'm saying 2e isn't low magic (I think we're all on the same page regarding that now) and 5e is pretty easy to go for the stated goals. It's just not that hard to say...
"The classes are barbarian, cleric, fighter, rogue, and wizard. I am using these optional rules. I have house ruled no cantrips or ritual casting. Here is the list of feats allowed. Here is the list of spells not allowed."
Paladin isn't necessary because of clerics, but if a person wants more fighter type allow EK and change the spells know option to be based on WIS and choose from paladin spells instead of wizard spells. Or just say "cleric".
I don't think 2e tweaking rules is better than 5e tweaking rules, but the 5e rules being more streamlined makes tweaks easier. I find 5e easy to work with.