Honest question - if you are not fussed about realism why do you want to slow healing down?
Because I want resource management that lasts beyond 24 hours.
I want the party's resources to wear down over the course of an adventure, not just over the course of a day. I want them to have to make decisions about whether they should press on our retreat. I want them to make decisions about how soon they should begin the next adventure.
And mainly, because I want TIME to pass in a sensible manner in the game.
Other editions were just as bad, but I'll use 4E as an example here:
It's expected to take 10 battles to level up. It's expected to have more than 2, but less than 10 battles per day. I'll pick 4 for the example (a fairly conservative option).
It therefore takes 2.5 days to level up. 2.5 * 29 = 72.5 days from level 1 to level 30.
Not my cup of tea.
I do want realism in some ways, but not in the sense of a realistic model of the body's ability to heal. I want realism in the sense that going from a newbie level 1 adventurer all the way up to level 20 or level 30 takes a significant amount of time. Otherwise, why would levels stop at 30? Surely a 600 year old elf could go much much further if he can do 29 levels in less than 3 months.
I'm all for healing being unrealistic in the sense that the value of daily healing is chosen based upon game flow/balance. But I'm not for it being unrealistic in the sense of 'magically' getting better overnight without the use of actual magic.
And finally, because I want magical healing to actually mean something. If you happen to have a cleric dedicated to the god of healing, I want that to have an affect beyond what happens during an encounter.