HMs are a good idea for the most part, but there do need to be some changes made. They shouldn't remove them for Key Items because it's a bit inappropriate to do something without your Pokemon. Furthermore, allowing you to delete HMs at will is also a bad idea because it can lead to situations in which the player becomes trapped. For instance, if you trade over a Pokemon that knows Surf before you get it, Surf to an area that cannot be left without it, and then deleting Surf. It's a stupid mistake to make, I know, but this kind of idiotproofing is necessary, especially in a game aimed at kids. I think the main thing they need to focus on is making them more useful, both in and out of battle. Inside of battle, they need to be made to be powerful and/or useful moves that people would actually want to use. To that end, they need to be a reasonable base power (I'd say about 60+) or useful in some other way. Furthermore, the HM list needs to be a diverse amount of types. Taking into account all HMs that have ever existed, we've had 4 Normal type HMs (Cut, Strength, Flash, and Rock Climb), 4 Water type HMs (Surf, Whirlpool, Waterfall, and Dive), 1 Flying type HM (Fly), and 1 Fighting type HM (Rock Smash). Now of course we only have a couple of these per game, but the diversity for each game is equally terrible. It gets a bit ridiculous for the Water type HMs especially, since it means that you have to load up your Water type with them in those games. To that end, let's see less Normal and Water type HMs and more of other types. As for outside of battle, HMs need to have some crucial function beyond the ability to clear random obstacles or warp to a certain area. Not every field move has been or needs to be an HM. So for the ones that currently are like that, they either need to be given more use or downgraded to TMs. With that in mind, here's my idea of what should happen to HMs:
HM 01- Strength: No real changes need to be made to this aside from possibly a change in type (Fighting, maybe?).
HM 02- Fly: Please give this move some better use. Being able to go back to practically any city ever visited is great and all, but still not useful enough to be an HM. What would be interesting for Fly is if you could actually explore the skies, similar to Dive but hopefully done in a way that could be considered unique (I don't really know how, though).
HM 03- Surf: Absolutely nothing needs to be done about this HM, it is without a doubt the most useful HM ever created.
HM 04- Dive: It was fine as it was in RSE, bring it back to its former glory.
HM 05- Dig: Making Dig as an HM would to a lot to help the lack of diversity in the HM list. It's Ground type which is something we don't already have, plus it has a lot of potential as a field move. A good use for it is if you could use it to create paths through loose dirt. For instance, if there's a rock wall in your way and there's no other way through than a column of loose dirt, you can use Dig to clear a path through the wall. Or if the floor is loose you can Dig a pitfall to a lower floor.
Cut, Waterfall, and Whirpool would be made TMs.