I think there are two problems. The first is that the simplest counter to healing would normally be ignite, but these 2/3 healer teams are generally running multiple cleanses and it's currently difficult to get the ignites to *. There currently aren't a lot of good ways to constantly mass apply ignites to the enemy team.

The second problem is that some of these healers/tanky characters do too much damage for how resilient they are. Sailor Sakura eventually starts hitting like a truck and is hard to kill. Nine tails chakra Naruto does crazy damage + ignite while having a lot of health and immunity to debuffs. Hokage Tsunade's mystery does a ton of damage + control, and while she herself isn't all that tanky, she's got reasonable defensive stats and provides a lot of team utility. This is the bigger problem since these characters have overloaded kits. If a healer can heal up all the damage that the enemy did and also attack back for moderate damage, why wouldn't you just stack your team with them?

The only way these teams seem to lose in non-mirror matches are successful control chains on all the healers so no one can cleanse, followed by enough burst to take one of them out. So these teams will probably die out when new ninjas are released that can either provide the necessary control/ignite spreading or quickly take one of the healers out.