Actually, we kind of left this when we left behind the "natural healing only heals 1 hit point per day" rules of 1e and 2e. In 3e, a character completely bed resting will completely recover from the nastiest wounds imaginable in a number of days equal to half his hit dice. A 9th level wizard will recover from -9 hit points to his max of about 27 hit points (average, no CON bonus) in TWO DAYS. A fighter will do it in 5 to 7 days, a barbarian in about 6 to 9. Under care of the heal skill? Even faster. That wizard under healing care, one day of complete bed rest, has gone from -9 to 27 hit points. Barbarian 9 with a 20 CON and 110 hit points can be back up and full within 3 days from -9. Not a twinkle of magic involved.
Contrast this to such a character in 2e needing a month to completely heal up. (rates accelerated after two weeks of bed rest.) So, characters healing up in a day's time isn't that much different from 3e.