I'd use some "Reply With Quote" options here, but that would make this message obscenely long....
Basically, I agree with both Random Person and JuiceJ regarding the nature of dowsing. Strictly speaking, it's optional, but it's such an omnipresent part of the game that it's hard to ignore. You don't have to swat a fly buzzing around your head, but more often than not, it seems like the right thing to do. Dowsing felt much the same way. (Not to compare dowsing's enjoyability to a housefly, as I found the former to be pretty enjoyable, but it hopefully gets the point across.)
As I said in an earlier post, I do believe dowsing should return, but with far more attention put on its optional use. It's perfect for things like buried treasure, but story objectives could be more cleverly completed with keener methods like riddles, environmental observation, and memorizing facts. It's true that nobody says you have to use dowsing, but when it's constantly prompted and promoted the way it is, it feels a bit like going through Mario Kart without using items or GoldenEye 007 without shooting anyone. No one says you always have to do it, but it's such an integral part of the game that you're shorting yourself the experience by not taking it.
In addition to dowsing's promoted use, it also acts as somewhat of a cop-out for smarter puzzles or more-engaging sidequests. Rather than immersing yourself in anything new, like solving puzzles, defeating hordes of enemy kidnappers, or unique mini-games, you're just running across the terrain until you find what you're looking for, grab it, and return to the starting point. That's not saying Nintendo can only use this approach for dowsing, but again, this is where dowsing should be rethought a bit if it makes another appearance. By coming across as entirely optional (like the Sheikah Stones) and not as a normal part of gameplay, it can be used to make the game a bit easier or, as per my preference, for finding small treasures across the world.
Long story short, dowsing should return. It would just probably be better if it was more optional. We have things like Sheikah Stones to help lost players, so dowsing feels slightly redundant unless Nintendo rethinks its basic design.