There's a whole Non Weapon Proficiency section (Chapter 5 in my PHB), it has like 60+ proficiencies. For example one of them is Survival, and you can use it to find food/water much like the 5e Survival skill. In the 2e you would roll a d20 and needed to roll under your Intelligence score, the modifier was 0, but as you gained NWP through leveling you could increase the modifer.
It's obviously different from 5e, but the ability score was still relevant even if didn't provide a direct modifier. The point is though that the old editions weren't just add-hoc DM does whatever they want for skills, it's little different from 5e in the basic gameplay. The player wants to do something, often times pointing out the proficiency/skill they want to use, then DM determines if a roll is required, and if yes the player makes the roll which determiens success/failure.
Yes the way the game evolved was to emphasize ability scores more then it did in the past, but the idea that anything that doesn't do it almost exactly as 5e does it will alienate a lot of people or wouldn't feel like D&D is nonsense.
My 2cents are that ability scores do matter too much in 5e, they should be relevant but not to the same degree as skill level, whether that's proficiency bonus, or something like 2e or 3e where you choose how to grow your skills. The other thing I'd want to make sure is that it's easy to understand and quick to resolve, this is something 5e does really well and I wouldn't want to lose that aspect in any new system.
Non weapon proficiencies were in the 2e PH and part of a whole chapter on proficiencies and had done out ability based mechanics for a lot of them (some were like feats in giving non ability based stuff). They were, however, explicitly an optional 2e system and not the only one. A lot of options were explicitly ad hoc the DM does most anything they want for rulings.
"Chapter 5: Proficiencies (Optional)"
"For a really complete role-playing character, you should know what your character can do. There are three different ways to do this: using what you know, using secondary skills, and using nonweapon proficiencies. Each of these is optional, but each increases the amount of detail that rounds out your character."
The three optional systems were 1) Using What You Know, 2) Secondary Skills, and 3) Non-Weapon Proficiencies.
Using what you know"
"One way to answer this is to pretend that your character knows most of the things that you know. Do you know how to swim? If you do, then your character can swim. If you know a little about mountain climbing, horseback riding, carpentry, or sewing, your character knows these things, too. This also applies to things your character might want to build. Perhaps your character decides he wants to build a catapult. If you can show your DM how to make such a device, then the DM may allow your character the same knowledge. Indeed, you might visit the local library just to gain this information."
"The biggest drawback to this method is that there are no rules to resolve tricky situations. The DM must make it up during play."
Secondary Skills
"Secondary skills are broad areas of expertise. Most correspond to occupations that your character may have been apprenticed in or otherwise picked up before beginning his adventuring life. Secondary skills are much more general than nonweapon proficiencies. They should not be used in combination with nonweapon proficiencies, which are explained later.
Every player character has a chance at a secondary skill. Either choose one from Table 36 or take a chance and roll randomly. A random roll may result in one, two, or no secondary skills.
"Once a character has a secondary skill, it is up to the player and the DM to determine just what the character can do with it. The items in parentheses after each skill describe some of the things the character knows. Other knowledge may be added with the DM’s approval. Thus, a hunter might know the basics of finding food in the wilderness, how to read animal signs to identify the types of creatures in the area, the habits of dangerous animals, and how to stalk wild animals.
"Like the previous method (“Using What You Know”), this method has strengths and weaknesses. Secondary skills do not provide any rules for determining whether a character succeeds when he uses a skill to do something difficult. It is safe to assume that simple jobs succeed automatically. (A hunter could find food for himself without any difficulty.) For more complicated tasks, the DM must assign a chance for success. He can assign a percentage chance, have the character make a saving throw, or require an Ability check (see Glossary). The DM still has a lot of flexibility."
Table 36:
Secondary Skills
D100
Roll Secondary Skill
01–02 Armorer (make, repair & evaluate armor and weapons)
03–04 Bowyer/Fletcher (make, repair & evaluate bows and arrows)
05–10 Farmer (basic agriculture)
11–14 Fisher (swimming, nets, and small boat handling)
15–20 Forester (basic wood lore, lumbering)
21–23 Gambler (knowledge of gambling games)
24–27 Groom (animal handling)
28–32 Hunter (basic wood lore, butchering, basic tracking)
33–34 Jeweler (appraisal of gems and jewelry)
35–37 Leather worker (skinning, tanning)
38–39 Limner/Painter (map making, appraisal of art objects)
40–42 Mason (stone-cutting)
43–44 Miner (stone-cutting, assaying)
45–46 Navigator (astronomy, sailing, swimming, navigation)
47–49 Sailor (sailing, swimming)
50–51 Scribe (reading, writing, basic math)
52–53 Shipwright (sailing, carpentry)
54–56 Tailor/Weaver (weaving, sewing, embroidery)
57–59 Teamster/Freighter (animal handling, wagon repair)
60–62 Trader/Barterer (appraisal of common goods)
63–66 Trapper/Furrier (basic wood lore, skinning)
67–68 Weaponsmith (make, repair, & evaluate weapons)
69–71 Woodworker/Carpenter (carpentry, carving)
72–85 No skill of measurable worth
86–00 Roll twice (reroll any result of 86-00)
