Well, since we got another mediocre rodent on the first route that could learn the worst of the HM moves, it didn't matter much even on my first playthrough, when I had an HM slave just because I was accustomed to having one. I slapped Cut on a Patrat, then later put Cut and Strength on a Watchog, and drug them around with me when I needed to. But by my second playthrough, I had started to figure out that we really don't need HM slaves any more anyway, though, to me at least, not so much for the reason you mention.
Honestly, if it wasn't for the fact that I've read other people pointing it out, I wouldn't have known that you didn't need HM moves (beyond that one Cut) to finish the main line of the game. I just wander the world, and when I see something that needs to be cut or pushed or surfed over or waterfalled up or whatever, I do it. Even if it's not necessary there's usually good stuff to be found so I don't see any reason why I wouldn't. And if I do all of that at the first opportunity I get, then when I go back to the same place later, I can be sure that I've already done it.
As I just mentioned on your reusable TM thread, even aside from whether or not one needs HM moves to complete the game, HM slaves are less necessary now than they were before simply because of reusable TMs. As soon as the Move Deleter is available (and particularly as soon as you can learn Fly), it becomes possible to slap whatever HM move you need on whoever you have available for just as long as you need it, then to just Fly to Driftveil, get it removed and replace it with a TM move. I find I do that especially with Strength. There was a time when being deep in a cave and finding a pushable rock and not having an HM slave with me only meant that I had to escape and get an HM slave and do it all over again. Now I just open the bag and click on the Strength HM and find out who can learn it and give it to whoever can afford it best - generally someone with a mostly unused TM move. Then when I get out, all I have to do is fly to Driftveil and forget Strength and relearn the TM and that's that.
Speaking of Fly though, I did continue to use an HM slave for Fly longer than for the rest, just because it's one of the most consistently useful HMs but it's still a pretty poor battle move. Most of the time I put it on a Ducklett/Swanna (along with Surf, though that's at least a decent move, in part so that I always had it with me and in part because Swanna actually makes good use of it). In my latest though - B2 - I've been using Fly much the same way as the rest of the HMs - just putting it on whatever can learn it and can afford to tote it around for a while, then forgetting it and learning something better in its place later.
All that said, I do sort of miss HM slaves though. I've had some great HM slaves over the years who are at least as much, and in a lot of ways even more a part of any "team" I've had than the best of the battlers, just because they were always there, day in and day out, doing their part.