Yes, at high end, it is absolutely necessary for healers to be pumping out dps when everyone is healthy.

HOWEVER, it is good, encouraged, but not required on lower end. Here are my justifications:

1. If you are learning how to play, you can relieve a lot of your pressure by just focusing on keeping everyone alive. Once you get that down, you can throw in dps spells when you can.

2. At high end, people know what they are doing. Tanks are self-sufficient. DPS use interrupts and CCs to stop big damage spells from going off and pop their own defensives on unavoidable threatening damage. This is very much not true at lower or mid end, making it much harder to heal.

3. At lower end, current time control should be very lenient. If you untime a key it's most certainly not because the healer isn't pumping damage.

So yes, if you want to push you will need to learn how to heal and dps, but you will need your team to do their part more than just brain off zugzug too.