It works fine IMO in 1e or similar, where there's 12 or so classes, two of which - Cleric and Druid - can heal. I should note, though, that I very much see Druids as simply full-on deity-worshipping Clerics with a nature focus, different spell list, and some different mechanics and restrictions.
Assassin-Thief are another pairing that work well sharing a niche and yet each being their own thing; ditto Magic-User and Illusionist (though there's room for at least one more in there, my choice being Necromancer).
Fighter-Ranger-Paladin is a bit messier. Fighter-Ranger by itself is fine as a shared-niche pairing, but Paladin can't make up its mind whether it wants to be a Fighter or a Cleric or what.
Monks are their own thing and have their own niche and identity.
By-the-book Bards are a waste, though there's space for them as an oddball class starting from 1st level like everyone else. The trick, though, is to design them in such a way that they are unique and not be tempted to shoehorn them in with the other casters like recent-era WotC has done.