No, there's scene-setting and plot-device magic and the occassional powerful magic-wielding villain in S&S.
Absent from the genre, however is the plentiful magic items and perfectly safe, versatile, daily casting of D&D.
I think people need to either visit the earlier editions of D&D or the many, many, many fantasy rpgs out there that have far more gritty healing rules than 5th Edition and get a sense of proportion.
Been playing D&D since 1980, the painfully slow natural healing wasn't 'gritty,' it was irrelevant, healing took place at the rate of the cleric re-preparing his spells. Unless you used the optional rule and had to take a week off every time someone dropped to 0. That was one of the reasons low/no-magic didn't work, and why the bandaid cleric was a strereotype.
Game pacing is down to the GM.
Not if he wants to retain the resourve-management aspect of the game, then it's dictated.
I have never once found gritty rules on wounds and healing, slow full recovery times or lack of MMO-style fast magical healing to make a game 'gruelling and un-heroic'.
Calling a perennial feature of all eds of D&D 'MMO-like' seems strange to me, but, then, I don't play MMOs, my impression of fast magical healing comes from decades of D&D. But, sure, you may like grueling and un-heroic, that's down to preference.
It is entirely misleading to state that a game will be bad with anything but fast healing rules
The game is 'bad' until the DM 'fixes' it.
In a standard high-magic game, slow natural healing just shifts the burden back to slots. So clerics (all casters with Cure Wounds on their lists) must devote more of them to healing, and the party must recover slots more often. Fantastic if you're playing a caster without that burden, but otherwise not the game at its most functional.
OTOH, if you use slower recovery across the board, for healing, slots, &c, all you do is shift the pacing, you to avoid a 5min work week instead of a 5MWD.
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Fast healing comes most often in D&D (in every edition) from magic, so stating that low magic doesn't mean gritty healing is a very difficult point to logically support in light of this fact.
Logically? If you want to invoke logic, you should refrain from blatantly begging the question and appealing to tradition.
Low-magic has been used many different was in the games community over the decades, from merely fewer magic items waiting to be found, to casters/items being extremely rare in the setting, but casters still part of the PC party, neither of those make fast magical healing unavailable, though in some editions lack of magic items could still be problematic in other ways. But, low-magic could also mean restrictions on the power of PC casters, or even no PC casters, at all, and that was distinctly problematic in all eds prior to 4e (the exception to so many 'you could never do that in D&D' generalizations), where it was casually seamless, a group could just happen to choose all 'martial' characters, and the game remained workable.
In 5e, HD and overnight healing mitigate some of the problems of doing without readily available, instant magical healing - but not if you flip on 'gritty' healing...
But the way to make even nerfed casters palatable to players is to make magic something rare, wondrous and even feared.
I agree, if from the reverse reasoning: in a low magic campaign, magic is rare, so both more wondrous and even feared, and a much greater advantage for those few who wield it, so it becomes even more important to 'nerf" PC casters.