Make your weapon sway more, but still, controllable. People without experience with firearms probably have shakier hands, less steady aim, probably can't handle heavier weapons for long, but it's not like they have fucking parkinsons disease which makes a bullet veer off 60 meters to the left. It'll be harder to control and manage, but not directly take away your input and make it RNG.
Honestly in Bethesda and Borderlands the inventory system is used to add an additional "level up" experience. In Bethesda games by either relating it to strength or having perks that allow you to carry more, fast travel when encumbered, and so forth. Whereas in Borderlands I spent a significant amount of time increasing my backpack slots because I would constantly run out of room in the heat of battle and didn't want to be making decisions about what to keep or toss mid-combat. When you're playing optimally, it's not just about upgrading equipment, it's about what is the highest value items at any particular moment. Those decisions do matter, and when done right, OCD nerds like myself get to feel smart and good about our choices as we see our wealth and gear improve faster than average (though that's a tough metric to understand unless playing with friends... e.g. You have HOW MUCH GOLD???). In the end though, harsh inventory systems are full of mechanics of burden, and in a day and age of instant gratification, twitch reactions, and little thought given to strategy, I think they're becoming less and less welcome. That said, I think they're an important part of RPGs in particular. Gathering materials and creating the perfect house in Fallout 4 or Skyrim would not have been as difficult or interesting without encumberance... So I think it would have detracted from my satisfaction of finally getting things just right. In Fallout 4 in particular, they put in the connected town inventories, and finally completing the full loop of that was very gratifying for a settlement junkie like myself...
I don't believe that contemporary encumberance systems are built with this in mind. If they were, they'd be far more limiting. Also I don't believe that harking back to a different type of game is a good argument for their inclusion. I find it interesting that you mention Borderlands, specifically, because I can't recall ever hating or feeling even slightly inconvenienced by the inventory system. It was easy to navigate and easy to use. It was easy to see when something was just not worth picking up. And, it was almost entirely just weapons, which makes a world of difference. I don't believe that it was the encumberance system so much as the fewer types of items that could be found. You were never given a good reason to pick up all the things. Money was far less valuable. I can't recall buying much of anything from a vendor unless it was something spectacular that I could afford at the time. If I couldn't afford it, it was no big loss because I would likely find something even better in the near future. A game mechanic should exist to enhance gameplay (imo), and while I can see how a limited inventory like you describe could be interesting, I don't see how it applies to current RPGs. Well, maybe Legend of Grimrock is a valid example, but again it is a different type of game, and the amount of things to be found is far less than you find in most other modern RPGs.
I’d like to chime in here to extol the benefits of a limited inventory. It forces a certain emphasis on tactical or strategic thinking. Unlimited inventory had an era in adventure games where items were frequently (almost always) solutions to a puzzle. When encumberance or space become no longer issues (Gamebryo engine with carry weight mods) then an entire gameplay loop of evaluation, optimization, and utility / crafting become severely truncated in relevance. When everything is there and available, it’s no longer a question of meeting a situation with available resources, but the precise tool from a comprehensive warehouse sized inventory. In Witcher 3, I never wound up using oils or potions...but because their components didn’t take up any weight, poor Gary of Nivea wound up burdened down by about a thousand cubic feet of flowers, bones, ashes...the world’s worst ghillie suit. (No wonder Roach had galloping problems). Preservation of the scarcity mechanic keeps grinding fresh because it forces you to keep changing up your tactics and approaches based on your current resources. Borderlands is a particularly good example of inventory management serving the essential loop—having played with mods where I could level my guns with me (legitimately acquired), it took a HUGE part out of the game, without which the combat alone was (much) more grindy and lackluster. As a holdover from D&D...with the increased options to the player, every extra thing is a nightmare multiplier for the DM. Even bags of holding explicitly were designed to NOT allow magical equipment (catastrophic explosions ensue) and they had limitations to discourage abuse with the whole airless thing. In conclusion, a limited inventory adds additional dimensions to the core gameplay loop, especially in a dress up game like a RPG where more good is had from gear than innate abilities.