I don't understand this. What is wrong with healers?
First, note that having a hero/champ that can heal is different from a dedicated healer, whose main purpose is to heal.
The short version: You get ridiculously boring laning when you have a dedicated healer that can essentially remove any aggression from the opponents. Not to mention the terrible poke heal meta that can show up.
In laning phase, this is more of a problem in League than Dota due to the nature of more spammy spells. Dazzle still has a heal right? But it's not very strong and he can't use it as much as he wants, so it's all right. Also he needs to use it on someone in the face of the enemy to fully utilize it.
Strong heals in general make the game more passive when they are just used to top up somebody's health. This is the reasoning used when League's heals are moved more towards heals that are more useful when used as clutch heals (i.e when the target health is low the heal is more effective), while being less effective as heals when the target has much health. Also, this is the reasoning why there are more shields in League instead of heals, since you need to time your shield properly to block damage rather than just healing after the damage is done. A shield will expire, a heal will stay there no matter what. Also, weaker heals with temporary armor buffs.
Many people in League didn't like how Morello disliked heals, but in the latest patch (4.5), the Heal summoner spell got a
buff. Now pros are running healing comps, and it is generally relatively boring to watch compared to before. People are now rightfully crying for nerfs to the Heal spell, which is completely reasonable. Morello's opinion is vindicated.