Yes, D&D requires healing. Without it, you basically have 1-2 fights a week, tops, which completely hoses the traditional adventure structure around which the game is designed.
No, it's not a good thing. It's by no means a necessary design decision, it's radically contrary to the source material (as nuts as it is to say 'healing spells' were thrown about willy-nilly in LotR, it's even more out there for the works of Howard, Leiber, Vance, etc. who Gary Gygax considered his most important influences), and it creates an arbitrary need for a type of character that a majority of players seem to consider less fun to play.