Yes. The most WHM has for a burst phase is Presence of Mind, which has us spam Glare still, but now FASTER. Previous expansions gave us multiple DoTs on all healers, and nothing 30s long, so uptime was something to keep an eye on more often. This is what people are asking for when healers complain about DPS being boring, it's currently monotonous, homogenized, and extremely uninspired.
As for getting in the way of healing, well we have a bevy of oGCD heals that let us just not interrupt our damage as is, the only way it would interfere with healing is if they went back to 2.5s cast times and gave us no instant cast options. It all comes back to how well they design the job. And good healers would know when to stop DPSing and focus on healing when things are going south.
I'd personally like some interplay between our GCD heals and damage kit, so that they don't feel like they're "fighting each other" but instead feel complementary. But that's another discussion.
In the context of healers, downtime refers to moments where we don't need healing. The incoming damage is typically separated enough in content (especially casual content) that you can get by with an oGCD heal, and spam your singular nuke until the next time incoming damage happens, which has us press a heal oGCD between the nukes.
The reason people ask for more DPS options on healers, (and note options, not extra damage itself), is because increasing the healing requirements in fights also increases the skill floor in completing that fight. By giving extra DoTs, a gauge to track, buffs to give, or whatever, increases the ceiling of healers while only mildly impacting the floor for less skilled players.