As a Healer main i'll try to explain why this isn't what should happen. We don't want to do more damage, and we don't want to have more health. We want our main focus to be healing, that's why we do it. There are plenty of other ways to deal with a healer rather than just killing them and ill try to provide examples while I go.
First: Chain CC
Use multiple stuns, slows, etc. to bother the healer, if they aren't super comfortable they will start to back off OR panic waste their abilities.
Second: Bait their support abilities
Put a TON of pressure on Kulev for JUST A SECOND, he will be forced to shield himself, then you switch to another Damage character. His heal isn't strong enough to withstand all your damage at one.
Third: Target Switching
This is key in games like WoW where the fights last a long time, you need to know when to switch and burst certain targets at certain times. Gizmo just rounded a corner and is seperated frome her healer? BOOM. Melted.
Fourth: NEVER FOCUS THE TANK
If the two people playing together are a good Tank and Healer combo, the Tank WILL live FOREVER. So you should never expect to kill him. Choose your targets wisely.
If you need some one to play with or just have questions feel free to add me!!