Myself, I kind of like the idea that medics in-universe are capable of honing their skills to the point that the gap between properly applied medicine and "Hurt-B-Gone" magic is much smaller than it used to be, although the gap is still present. Medicine can whiff a lot harder than healing magic, for one, and even with investment it takes a lot longer than ol' Hurt-B-Gone, especially in groups. Somebody that trains extensively in medicine being able to meaningfully heal wounds with their skill checks is good, in my view, and the fact it's something anyone has the capacity to train in removes the feeling some groups have that a party member with healing spells is mandatory to allow the party to progress through multiple non-speedbump encounters a day. For the most part in 1e wand of CLW was unquestionably one of the most useful adventuring devices while healer's kits were pretty useless without skill unlocks or extensive houserules; personally, I like "the party takes a moment to let the doc bind up their wounds and ensure everyone's fighting fit" as an image more than "the party groups up as the designated wand-wielders break out the stick o' life and magics all their injuries away."
Magic is still unquestionably what you'd do for in-combat healing in my book; even if you have Battle Medicine, healers' tools take two hands to use which means a ranger who's also a field medic is going to have to make some quick decisions vis a vis his crossbow and an injured ally while the guy with a Heal spell does not.
Making it easier for parties to patch up and keep going makes for longer adventuring days so you don't have to keep retreating from dungeons to rest, which just disrupts flow and isn't any fun. The GM will use the time needed to heal up to complicate the situation if they're wise, while the party doesn't feel like a bunch of babies who have to bail on a dungeon after a few rough fights or risk future encounters being more than they can handle.