I'm asking what value that gives. Why this enhances the experience of play. Boiling down your post to its core points, you have simply said, "Yes, it is annoying, but it it still valuable." But I was asking why and how it is valuable, questions you never answered. Well, apart from the "it gives Strength value," which as I said is really a condemnation of how bad D&D stats are, not how encumbrance adds value to the experience. We tolerate rules that pose negative impositions because they do something worthwhile beyond the frustration. What is that, for encumbrance? Because the value gained from the price paid looks ever more dubious to me.
Encumbrance is a limitation. Limitations by itself invite creativity and are necessary. That is the reason we are playing D&D and not "make up a story without any rules".
In the special case the limitation of how much a character can carry gives the game strategic depth, invites dilemmas and problems to solve and makes the game feel more realistic.
Now the characters have to make strategic decisions on what and how much to carry of. Or if they get like a donkey to have more carrying capacity, but which also makes them less stealthy and the donkey can't or will not go into certain areas.
It put (depending on the Game) soft and hard limits on how far and quickly you can explore or travel.
Without encumberance, the rules for eating and drinking, the tracking of resources like Torches, Rations, Arrows ... you remove the strategic game aspect of exploration.
The interaction of encumbrance rules with the rest of the world creates the exploration game itself. Without that rule, there is no exploration game. It would devolve to just "I look for that thing in area x until I find it or until random encounters kill my group".
So, let's put it in an example, because most the rules discussion are useless unless you put them into a concrete context.
Our group of adventurers (heros) is tasked with finding the lost temple of Exemplia in the jungle of Hereitcouldbia. Their is a rival group (rivals) of adventurers also looking for the temple.
Now, what will the heros do? No matter if we use encumbrance and mundane ressource teacking or not, our heros will do some research to narrow down the area they need to search in for the lost temple. They did that. Now the narrow it down to an area of like twenty 6-mile hex fields to search. 10 of those are desperate, 5 are jungle, five are swampy. The area is like a 5 day travel away trough a jungle area.
Now, without encumbrance, they just go and search every hex field until the find clues.
They will have some random encounters like hazards, monsters, the rivals, other nocs, other ruins or cool locations, that will give clues and so on ... and unless they TPK by one of those encounters, they just heal, long rest and continue until they find the temple.
Now with encumbrance and ressource tracking, how will that adventure turn out?
First of all, they have to plan the expedition. They have to gather resources. They have to plan on how much food and water they bring. Will they decide to forage? Do they have somebody with the survival skill to navigate and somebody else with the survival skill to search for food and water? If not, do they have to hire an NPC, that helps with that? Do they decide to use spell slots (ressources!) to create food and water or do they decide that that is something they will do when they run out of other resources? Do they even have those spells? So they buy a donkey, a cart or hire NPCs to increase their carry capacity?
So let's say they want to travel lite. They don't trust the Hirellings in Adventuriatown and a donkey would slow them down. So they pack what they can. Rations for 20 days, water for 5 days. They think they can find enough clean water in the jungle.
They only have on guy with a survival skill proficiency. This guy navigates. So they don't have anybody to help with foraging.
But after 5 days they arrive. The have 15 days of food left and no water.
Now the one guy with the survival skill is looking for water, while the rest searches the first hex.
He finds a stream that seems to be clean, they can refill the water. They don't find anything jn the hex. They go to next hex. Search. 14 days worth of food. Oh no, a random thing happens ... rats go I to the food. Now they only have 6 days of food left.
barley enough to travel back! The survival guy is searching for water and food. He can just find enough for one day.
They continue to search. Now they don't find anything in the lush jungles. They barley have enough food to travel home, but the lost temple must be in the desert area. But they know, in the desert they will probably don't find food. Now they have to make decisions. In the meanwhile, they also have all those other random encounters our non-rncumberance group has. Maybe they meet the rivals who have a lot of food. Do they maybe steal from them? Or do they trade with the random NPC they meet?
Because of encumberance and resource management, the game got more depth, more realism, more decision points, a heightened difficulty. It improved the same scenario tenfold.