In all honesty, I'm hoping that bottle caps will be difficult to obtain, so that breeding will remain the most efficient way to get a competitively viable Pokemon. IV breeding has gotten much faster and easier in the past couple generations, and I feel like it's a worthwhile post-game activity. I'd be sad to see Hyper Training replace it.
That said, I'm really interested in the possibilities of this feature! I suspect Hyper Training will be very useful for specific Pokemon, ie: legendaries, event Pokemon, your starter (and other Pokemon used during the game's main storyline), Pokemon transferred from Virtual Console RBY, shinies you find in the wild, Pokemon received in trades as gifts from friends... Basically, Pokemon that can't be IV bred, and Pokemon that hold a lot of sentimental value, will have the potential to become competitively viable. I like to play competitively, and I do breed for IVs to get viable Pokemon, but I also hold onto a lot of weak Pokemon just out of personal attachment. I'm eager to see if Hyper Training can bring my "casual" Pokemon up to par.