I'm actually surprised no one is actually questoning WHY the HM system is in place the way it is. There's a very specific, game breaking reason why they force you to not delete HMs and thats' because there are HM moves that can be learned by some pokemon via level up OR you can transfer pokemon who know certain HM moves:
so say you get to the point where you get the appropriate badge to use a move in the overworld map (let's take cut for example) you have a pokemon from an old game that knows Cut (and since people will fixate on Cut specifically, you can also subsitute ANY Hm for this same scenario) just for the heck of it, you start cutting away to get certain items, you level up, learn a better move and delete Cut and then oh look! You're late for school or work, you save and quit, come back later and start your game up again and oh no! Once you start your game up again all the trees have respawned and since you deleted Cut, you can't get past them because even though you got the badge, yo didn't go to Cutter's House first so now you can't teach anything in your party Cut (or whatever other HM move got you stuck somewhere) and no you need to reset your game and lose the 2, 20 or 200 hours you put into it for a simple mistake that can happen to anyone. THIS is the reason the HM system is in place. in the original Hoenn games if you were on Dewford and had a pokemon with Surf in your PC the game would prevent you from releasing that pokemon from your PC if it was the last one in your PC that knew Surf, even if you had the HM in your items pocket because if you lost all the pokemon that knew Surf in Dewford, you were trapped and could not get off. It's actually an extremely well thought out system.
The same thing happens when you encounter Latias/Latios and you have a full party. If you send the pokemon back to the PC that has Surf, you're now stuck in the other side of Hoenn until you get all the way up to the weather institute and get access to a PC again.
I would MUCH rather be inconvenience by having to find someone to delete the move than not pay attention briefly and lose a move that makes me have to completely restart my game all over from the beginning. For every 1 person complaining about having to delete the move, I can guarantee there would be 1000 complaining if such a game breaking system was allowed to be in the games because LOTS of people (particularly young kids) could quite easily make these various mistakes.
I'm sorry this doesn't make sense to me, in fact I'm not even sure I follow.
So in this hypothetical scenario, you went the entire game without receiving the Cut HM from the Cutter but instead traded a pokemon with the move to your game. Then you deleted it after a use and saved. I fail to see the irreversible dire mistake here.
1.) Why would anyone NOT stop by the Cutter's house for the HM even if they were trading over a pokemon that already knew it. You can actually do it BEFORE receiving the Stone Badge and its not a tedious effort.
2.) If the move was removed from the traded Pokemon why can't this hypothetical player just return to Rustburo and obtain the HM or does the Cutter stop giving it out at some point?
There is also another flaw with this scenario. Unlike in Kanto and Sinnoh which both have at least one required area/route blocked off by a tree every single area in Hoenn that is reached by cutting is optional. One can complete the games without using cut a single time.