This is not really true. Poisoning/Bleeding gets healers of important targets like Prince or Mercenary contracts. You can also convert people that you have poisoned early to have a “confirmed” convert, if you know there are plenty of healers alive or just convert the healer who has now “proven” himself, but cannot prove himself on the spot and thus does not have to. Of course, with Alchemist being a thing, that is a bit more difficult to realize. In an alternate case you can also poison/bleed a suspect of being Sorcerer, so that they can signal back and you know each other with DN’s, but that is a bit too fringe for the majority of players. Another case is that you can poison somebody as you are being put on the stand, while you claim a healer role. You can “heal to prove” and possibly live another day. Healers can also be overwhelmed if Hunter/Butlers get overzealous and you can possibly occupy/redirect them, if you know of them.
I just mean to say that the blanket statement of poisoning/bleeding before all healers are dead is stupid is not true.