Not having Accuracy doesn't stop you from doing dps. You may see a much lower dps, but you can still do it during your downtime. And you will still help your party progress.

Your dps just won't be so game-changing that all the content becomes one grade easier.

Healers can still do dps. The lack of Accuracy on healing gear is an adjustment which mostly affect your raid dps. It means against raid targets, your influence on raid total dps is curtailed to conform to the original design intent.

If you want to dps in raids, just do it. Yes your parse won't be so high, but that is how it should have been in the first place. Not having accuracy doesn't mean now raid content is boring facerolls. You can do exactly the same things as you did before, nothing needs to change. You can still be as busy as you want.

In fact, this now opens up an even more advanced level of play for healers who can adjust their gear to have Accuracy yet still heal perfectly fine, while at the same time dealing dps that other healers can't possible achieve. Kind of like how tanks have been judged for a long time. Survivability and dps. Now healers get to play that game, too.