That's what I'm proposing too. Where I think we differ is that I want all SR features (new and old) to not require more than one short rest per day for the class to function. If you get 2 or more, great, and if you don't, you don't feel cheated/screwed. Psionic Energy Dice (Soulknife and Psiwar) are a great example of this - you benefit from every single SR, but if you get zero you can still contribute for a full day.
A lot of the time it does, but not always. And I think the campaigns where this is never a problem don't have anything to worry about either way, so of course they're going to concentrate their design on the tables having trouble.
Not a potion - but Scroll of Catnap?
In a lot of busy jobs, you're lucky to get 1 hour-long break per 8-hour shift. Some don't even give you 30 minutes uninterrupted (though that's illegal in many jursidictions IIRC). So it's not unheard of, and that's without taking into account any of the scenarios I mentioned earlier where time might be of the essence due to the situation itself.
Now, I agree with you that the time per short rest can be tweaked to compensate, but that starts to run into other balance considerations like Warlocks maintaining multiple hour-long buffs when they're not supposed to be, etc.