As long as everything is civil, I enjoy discussing every idea's merits.
Water in Elder Scrolls games is a good point. What I mostly remember about it is that it is only a mild impediment, even the roughest river can be swum safely, in the heaviest armor; only animals made it dangerous, and only its speed reduction made it annoying. Just diving into white water is the kind of thing only an extreme sports enthusiast, someone who is desperate, or who carefully plans would attempt in real life. In Man Versus Wild, when Bear Guiles crosses a river, it is always a very dangerous undertaking, which, in cold environments, risks hypothermia, not being able to get back out, or injury by hitting something in the water. In hot environments, animals, and disease are the dangers; and in water fighting is difficult. In fload scanerios, a depth of a few inches of water moving at high speed is enough to move a car, and constantly trip and batter a person.
For water bodies to be something worth modelling, short of interesting water craft, I believe it has to pose a true hazard which bears serious consideration. With physics, the danger of being slammed into rocks is a good danger, and can make finding purchase against a cliff or ledge more difficult. Assuming a European themed land, low water temperature should rapidly sap strength, and cause dangerous lingering effects. Moats can have disease which have a chance of causing wasting sickness, as castle latrines usually dumped into moats. Rivers downstream from cities could have a similar risk.
Depending on water depth, characters should become more encumbered as they enter progressively deeper water; water up to the ankle would slow sword fighting, but not as much as if water were up to the knee, or arms. Swimming should defeat the encumbrance effect, but only if a character's buoyancy and strength allow for swimming; otherwise the character can only walk in water, and hop to the surface for breaths, or perhaps use a reed for breathing; but swimming should greatly limit fighting options (perhaps daggers and fists only). As proposed before, simply bundling armor, or perhaps any item, removes the weight penalty in swimming, under the assumption of buoyant bags. Bundling armor would take minutes of time in-game, so it's not a spur of the moment decision if danger is near. However, the ability to dive into water, and shed armor could be thrilling as an escape method; you would lose your armor, but if you could remove the armor within a breath limit, then you would start swimming, instead of drowning. Perhaps another dynamic could be wet and dry clothing; cold wet clothing prevents stamina recovery if suffering cold effects, unless it is wool, which is one of the few, or only natural, materials which can retain heat when completely soaked.
The utility of water is it becomes an effective non-structure based barrier, or extra defensive line, with a variable chance of circumvention. The importance of bundling items for swimming is that it allows water to be crossed, otherwise people would have to leave their gear behind to cross water, and no one would ever cross water in that case.
If swimming isn't seen as worth while, then at least having the gradual encumbrance modeled would be worthwhile, as would chilling, if the game takes place in cool enough temperature, or with mountain water. Disease also make sense to include. Not using bagged item swimming is more realistic, and even light armor would be too heavy to swim with. It also means not having to ignore the ability to swim with dozens of pounds of gold on your body. This would still leave room for bodies of water with variable depth, which can be crossed with deep wading, and water velocity mattering in regard to whether or not you will be swept away.