For immersion, it's my opinion that walk and run speeds should be tied to an equation involving variables of strength, endurance, weight of items carried in a container, and weight of items worn and carried proper.
This would work well with a hot-key container drop with a container system that allows you to drop the whole backpack, bag, dufflebag or whatever while still keeping proper carried items, and worn items on the character.
That way, with an equation, instead of the old pick-up-a-spoon-and-suddenly-over-encumbered mechanic, a character could carry light loads longer as a function of strength and endurance, while heavier loads might slow the character down, and cause them to get slower over a gradual progression of endurance decay.
With a droppable container system, a slow-moving character carrying a lot of weight could hot-key drop a backpack container to move faster during combat, and then pick the backpack up again afterwards.
Food and drink items could have more of a benefit value to strength and endurance equation carrying than for health, where taking a break, dropping your backpack, and sitting down for awhile with a snack and drink would also benefit a character to travel longer with heavier loads.
All this, of course, is more realism and immersion than most folks that play video games would like, and it's doubtful anything close to what I've described will be in the vanilla game. We will likely see a similar encumbrance system to Skyrim with some minor variation.
As far as variable, adjusting walking and running speed, it's my opinion that such a thing should also be tied to the stealth and sneaking mechanic where someone walks and runs differently in a sneak mode than they do when they're not sneaking, and different speeds of sneaky walking impact chances of getting detected while sneaking depending on sneak speed, movement, type of armor worn, and bulk of items carried.
That could tie into a container system too, where if you want to be sneakier, you drop your backpack full of wasteland loot, maybe hide it in some bushes or under some generic environmental clutter, and then proceed with being sneakier, coming back later to pick up backpack.
This kind of stuff has higher likelihood for getting added with a mod, than anything vanilla.