Honestly I do to. I love the overworld effects of HMs, and Rock Climb was really fun to use in the overworld; the way you'd just go zooming up the mountain, bringing an entirely new area into view that was previously hidden. I just wish HMs weren't SUCH a pain in the Arceus to put on my pokemon. Also, the "HMs can't be deleted" is an obsolete safety mechanism that prevented players from getting stuck back in Gen I when you could actually deposit HMs into your PC. Since you are no longer able to remove HMs from your bag, there is no risk that you'll delete an HM move from a pokemon in your party and be unable to reteach it when you realize that you're stuck, since you'll still have the HM with you.And we done this Unpopular Opinion yet: I like HMs. Yeah, you heard me. I LIKE the HMs. And I like the selection of HMs they gave us even though half of them are Water-type. Now I'm not crazy, the HMs main problem is you can't delete them and a few of them are rather weak (which wouldn't be a problem if you could delete them). But I like the idea of needing to solve natural obstacles in your path with using your Pokemon's skills, showing that as long as you're together you and your Pokemon can overcome any challenge be them a battle or natural barriers. This is also why I like the Trick House, sadly HMs for the most part are a one and done thing so having an extra area require you to use them again is welcomed. Though at the same time I still feel they could do more with HMs, not only with possibly new ones but explore what you could do with the existing ones. Like imagine while Surfing you found a rock blocking a waterway, you use Rock Smash to break it and suddenly the water level rises giving you access to new areas! Or using Strength and Rock Smash to do weight puzzles. Using Strength to force doors open or Cut to cut a circuit. Defog could certainly blow away more than fog. And think about the uses for these HMs while underwater using Dive! There's a lot of potential for HMs, which why I'm sort of sad they might be going in Gen VII but at the same time the PokeRide look pretty cool (though I'm hoping there would be someway to make some of our Pokemon into PokeRides? Probably not, though it does take away a bit of the bonding idea when you're clearing an obstacle with a Pokemon that isn't yours).
And also yes, I agree, when you delete an HM move I think you should still be able to use it in the overworld. Damnit I don't want Surf on my Gyaradose or Azumarill. That's just so pre Physical-Special split.