To add to
@Eleannor 's excellent historical summary, Blizzard's design philosophy fundamentally changed in TBC 2.4, when they combined spell damage and spell healing into spell power, so that healers could do more damage. Blizzard attempted to regress this a little in MoP with the introduction of PvP Power, a PvP-only stat that augmented the damage of dps and the heals of healers, but then "removed" the stat in WoD, and cleaned up most of the remnants by the time Legion rolled around.
Before 2.4, a battleground healer primarily kept themselves and teammates alive and offered battleground utility (slows, CCs, DoTs to keep rogues from re-stealthing, etc.). After the change, healers could more easily wear down a single opponent, but still struggled mightily in 2v1s. That made the most sense to me -- a battleground healer should always be able to 1v1 a dps
given enough time, and it's on the dps to either lockdown the heals, or coordinate with a teammate.
If a single dps can easily kill a healer, then there's no point to playing a healer -- you'll do your team a better service by playing a dps, which was exactly the problem with 19s and 29s in Wrath. Likewise, if your healer can come close to doing dps-level damage, then there's no point to playing a dps -- you'll do your team a better service by playing a healer, which arguably was an issue in BfA.
I haven't played in ShadowLands yet (fix the daggone L/R macro problem, Blizz! It's been three months!) so I can't speak to current healer power, but I get the sentiment behind the original post. While I don't agree that a fully geared healer should struggle against a single mediocre-geared dps, I do agree that more distinctive roles in battlegrounds made instanced PvP more fun.