Yeah, have to agree, if your story is as you say - asking them to kick the bad healer is fine after said healer has demonstrated such poor performance that it is impacting the raid.
People are always so afraid of using vote kick, but it's there for a reason. Every player needs to understand that if they suck so bad it stops progress in a dungeon, they can be kicked and it is their fault. If you cant be bothered to learn the game and try to play it to an ok manner (which is incredibly easy for FFXIV due to the low skill floor), then dont get shocked and b.hurt that you get called out and/or kicked.
Someone sucking at the game and preventing other people from enjoying the content isnt acceptable. People need to really switch the way they think: It's better to be the carry, than get carried.
