Its funny, D&D Beyond and VTT character sheets make tracking encumbrance easy. But we still barely pay attention to it. I find I am a complete hypocrite when it comes to encumbrance. I like the idea of tracking it but I don't enjoy enforcing it in practice.
At this point in this old DM's gaming career, I employ the "eyeball method". Now and then I'll eyeball it and if a character is looking kinda silly in how much stuff s/he's carrying around, I'll apply encumbrance penalties. If the player objects, I am completely open to changing my mind. They just need to show me the calculated weight and where they are carrying everything, that what they have in packs and bags of holding fit according to weight and volume limits. Generally, most players will just accept my ruling than bother. Those that don't are using digital character sheets that make tracking encumbrance easy and they pretty much police themselves.
I've never found the need to come up with a slot-based system or other alternative way of tracking encumbrance. All are much more work for me than my eyeballing it and much more work for the players, because D&D Beyond and VTT character sheets support RAW encumbrance rules for 5e out of the box and calculate everything.
Even if we were running 5e with pencil and paper, I would use the P&P Eyeball Method, which is the DM eyeballs it with the occasional debate over why it is logical for the gnome to carry the content of a castle's armory on his back. If encumbrance became such an issue that I would need the players to keep strict weight records, or records slots, on their paper character sheets, I'd probably suggest that I may not run the type of game they would be most happy with and suggest they they join me when I next run a game that uses digital tools.