We technically have this dynamic now with DNC who's identity revolves around buffs and can also provide very mild sustain. I do play DNC now and enjoy it, but I would rather be playing SGE with the fantasy that it is entirely capable of delivering upon. So in short, I don't think anything would change. You'd get some players who'd accept the DNC identity, but you'd still have a lot of vocal backlash against the healer role for feeling stale in easier content. It would still probably be looked at as inherently flawed by many dedicated healing players. The game would also need to output damage constantly in order to justify the healer role and not have the meta kill it for a 2x support scenario you mentioned, and who knows how that would impact MSQ instance content. You'd probably just have a different game entirely at that point. Perhaps if the frequency of damage was high enough to actually justify healing rotations, it might not be as frowned upon, but it's too difficult to say because the environment would have to be entirely alien to the one we have now.
The reality is, that idea of healer is one that is dying because it was historically very unpopular in older MMOs where healers were HP batteries and little more. Most people don't want to just be a battery or a cheerleader. They want to engage with the gameplay, just from an angle of someone who prioritizes support and needs to make decisions based on the situation their in of when to attack, when to heal, when to support, etc.
Now I know the point of this was for the sake of argument, but I do want to point out that while many of the suggestions several of us have made over the years about the healer role may be a lot for the tepid constitutions the devs seem to have around healer design, that these are suggestions would work within the structure that this game provides. It doesn't require a ground-up rework of the game because we discuss changes that work based on how encounters are designed currently. We need to accept that DPS is a major party of healer gameplay in this game as it has been designed, whether intentional or no, but I also believe that this acceptance can also lead to creating a healer that is meant to appeal to the healer that doesn't like offense--a healer who disguises their DPS contributions through support.