Be it as may, a shaman healer has an Interupt that other healers do not. That fits your description of “giving them an edge” above other healers, it’s irrelevant if dps have interrupts, it’s a comparative strength against their peers.
Of course people don’t actively seek shamans. I don’t recall seeing any group specify any healer type ever, because the healer role is not one people tend to be picky about in pugs so long as the healer has done the content. Dps have their relative strengths in their damage, and as you get to pick three, you optimise. With healers and tanks the same doesn’t happen.
I seem to have interpreted the word strength differently to you. You state arms doesn’t have burst as a strength, as DHs can do it too. That doesn’t negate that arms can do it however, strengths of classes are not a zero sum game. If we’re talking someone only one class can do, that others can’t, I’d be thinking of a word like niche.
And if we’re doing that, we may as well park the healer conversation at druid, because they’re tuned so highly above other healers atm in high mythic that if we’re talking “who does it best” then using that definition, no other healers have any strengths compared to a resto druid. I’d contest that definition of strength.
Multiple classes bring similar strengths. Some bring more than others, so they’re valued overall, which is why arms is not a must have dps for example. But arms is still good at burst AOE. The issue is DH are good at that and several other things. It doesn’t remove that as a strength of arms, it just makes it so that alone isn’t a reason to pick arms because other classes have that strength plus others, and obviously you pick the classes that bring the most strengths.
Players who wanna play off meta however can still make it work through those strengths these classes possess.