Just because the rules don't list a cost doesn't mean that a bandage or a shot of whiskey can materialise out of thin air at the character's convenience. Don't gloss over acquiring it – it's not that kind of game.
A shot of whiskey comes from a bottle or a cask. A bandage comes from a first aid kit or has to be made. If they previously established possession of either, great! They're golden.
If not: Where is the bottle or kit? How do they get to it? What stands in their way? Is there one at all?
Without having it already established as to-hand, they'll have to go get it, find it, make it, buy it, etc. There may be no obstacles at all, but they still have to exert narrative effort and create some movement in the fiction. Tearing a strip off their shirt for a bandage is easy, but now it's established that they're wearing a ragged shirt. That's important! That is the game.
Once they've started to move in the fiction, they may trigger moves in the process of trying to help themselves. That's part of how moves snowball: harm needs to be dealt with, which creates fiction, which might trigger moves, which makes fiction, which triggers other moves…
But even that's easier than arranging for weeks of bed rest, so why ever use bed rest?
Damage isn't just ticks on the Tracks. Remember that "Harm can be either general or specific." (p. 25) That means that if you've taken harm from poison, a bandage is narratively inappropriate and won't heal any harm. You're going to have to do something other than a simple aid, and that just might mean laying up in bed for two weeks.
Ditto if you're recovering from a complete mental breakdown. Once you get down to 2 harm a stiff drink is just not an appropriate fix for the remaining madness that ails you. (Maybe three or four or twenty… but at that point, you're not actually recovering are you?) In those circumstances, you're not just a little shaken up from a nasty surprise, you're still shaken up from the memories of the horrors that deranged you. The fiction just doesn't allow a stiff drink (or equivalent) to remedy the problem: you've got to stick it out in the nice, quiet, bland mental ward until you're well. A stiff drink makes sense on the way up the Sanity Track, but it doesn't make any sense coming down from the higher segments.
And besides, bed rest may be the only fix available. Trapped on an island à la Agatha Christie's Ten Little Indians? There may not be any booze available, stiff or otherwise.
But if the fiction doesn't say that bed rest is better, or the only option, then yeah, a Simple Aid is going to be preferable. It's not obvious when just looking at the rules, context-free, so it helps to remember that the action during play is not always so cut and dried that players can always pick the context-free-optimal choices as they please.