My biggest hope for DLC is much more involved shrines. I love the shrines, but this time around it seems like they leaned towards the shorter side of things, which I appreciated since they are a means to an end (getting more life/stamina) than the core gameplay experience that we get from the rest of the game. That being said, I do love how limiting they can be, and those limitations force you to consider the game from a different angle. I'd love a series of larger shrines with multiple components needing to come together to make progress within each one. I don't need them to be as large as a traditional dungeon, but perhaps closer in scope to a divine beast.
I'd also like to see a series of challenges/races for your builds. TotK gives you so much freedom that many of the things you need to accomplish can be done in a variety of ways and at some point the challenge drops a bit. Challenges and races would put limitations on what you have at your disposal for crafting as well as limit the amount of time you have to perform each challenge.
Adding to the previous idea, I would love to be able to race head to head with another player in these challenges/races. Give players a set amount of time to create their builds, then start the clock as both attempt to reach a specific destination. This could be done in the over world, but could also be done in more of a closed shrine setting.
I also like the idea of doing more building/restoring of Hyrule, as someone mentioned before. There are so many ways to go about this, including requiring certain resources to build various rooms, or the need to barter with different villages for the use of special rooms that could be used in construction. You could also have to find various rooms and/or furniture scattered across all of Hyrule.
I honestly think there are a lot of spinoff titles that could emerge from the world they have created here and I'd love to see Nintendo almost treat it as its own IP. It's no wonder the developers decided to return to this engine and this Hyrule after all they work they put into it, and we can see how flexible it is for evolution. throw a couple smaller teams together and let them create some wacky, zany experiences while the next mainline Zelda is being cooked. We've got 6-10 years until the followup, and as much as I love HD remakes of the older titles, I wouldn't mind a few quirky spinoffs to tide us over until the next main course.