Underwater traversal is a woefully underutilized feature in many video games. The opportunities for exploration and discovery it affords are pretty tantalizing.
There are two stipulations to make it work, however.
1.) Controls have to be fluid (u c wut i did thar?
) Nobody wants to fuss with cruddy swimming controls.
2.) There has to be sufficient challenge to diving underwater and sufficient reward for doing so.
I honestly can't think of a game that has managed open world underwater exploration well. The Witcher 3 has a lot of it but it's poorly executed.
Geralt can be underwater only for as long as he can hold his breath (or much longer if you take a potion). The breath mechanic just puts a timer on the amount of time you can stay underwater. There's no challenge. Just an annoying limiting factor.
There's also nothing to discover. Most of the diving takes place in the Skelliger isles and it's all just a painstaking menial collectathon.
Otherwise, Geralt only dives underwater to get at loot or quest items or as a way of getting from A to B that doesn't involve walking.
What if there are pickups underwater that will increase your breath and allow you to stay submerged longer? Perhaps once used they only return on a timer. This would make players have to carefully manage their available breath and pickup resources while diving. Perhaps items or pickups could pause breath consumption momentarily, or extend the maximum amount of breath for a while? This would at least make diving more challenging.
As for an extensive underground. Yeah, that's kinda in the Zelda series' identity. I'd love to see a vast interconnected subterranean network, perhaps one that can be explored in isolated parts accessible from the overworld but can be connected by exploring portions accessible from other parts. Throughout the course of the game, Link would have connected a vast seamless underground complex - perhaps even linking individual dungeons or acting as a fast travel network as well. Think of it as not just several individual dungeons, but several individual dungeons that become one massive dungeon over the course of the adventure.