typo: said pope trick, which is a very different spell...
Good for you I guess? I think from a rules design perspective, or as I mentioned earlier a sort of meta rules perspective, this is a healing spell. I'd expect people in-game to describe it like you describe it because it's sort of pulling back the curtain on the rules to talk about this spell in terms of it filling a healing niche, but I genuinely think it does just that. And that doesn't change if you or others view it different, does it?
From a meta rules design perspective, is it a "healing spell"? Again, I would say it's a flexible utility spell that
can be used to heal. Or mitigate damage by removing a character from combat. But it can be used for a number of other purposes, such as hiding and spying.
As a legacy spell,
rope trick was one of the first spells updated. It appears as early in the playtest as packet 2, the first with character creation rather than pregens. However, for most of the playtest it was unchanged, even after short rests went from 10 minutes to 1 hour in packet 6.
When the spell was designed for 5e, having to find a "safe place" to take a short rest was less needed as 10 minutes is a relatively short period of time. People felt comfortable doing that anywhere.
Pulling back the curtain, the spell existed in 1e and 2e (in the PHB) when there was no short duration healing. The "design" of the spell has nothing to do with short rests and everything to do with replicating the Indian rope trick illusion:
https://en.wikipedia.org/wiki/Indian_rope_trick
You'd probably have to go back to the player at Gary's table in the '70s to ask if they designed that spell as a "healing spell" and a place to rest and recover, or if they just wanted to do the cool magic trick they had read about...
As
rope trick was a wizard spell, it was potentially planned as a way to escape combat and avoid taking additional damage. Low level wizards were fragile. But the long duration (20 minutes/ rounds of combat per level) and given it's a 1e spell probably created by Gary's players for his various Greyhawk campaigns, mean ambush tactics were likely part of the original design. You cast
rope trick, hid, waited for a guard to pass, and then snuck past for the treasure. Or dropped down and killed them before they could fight back. It was a spell to negate combat and bypass the danger and get to the treasure.