I think the issues arise because playback is incredibly easy to misuse, and also because the mimicry is uniquely unfair to a bird.
Birding can hardly be described as a zero-impact activity on the birds anyway, but the birds have to occupy a world inhabited by big animals including humans and therefore recognise these as such and avoid when they feel threatened. So the impact of birders going around a reserve isn't a particular issue. Birds have had thousands of years to adapt to other creatures.
Playback, on the other hand is a sneaky use of our superior technology to create a virtual bird, of the desired species, in order to make the bird appear and do something. It does nothing for the bird, and makes it perform for us. It is a technology that has only really been practical for the last 10-20 years or so, so it is new to birds. Okay, you can say those of us who feed garden birds also make them perform for us, but the birds do this electively and they get something out of it - easy food.
Playback has added to scientific knowledge and has been used in field ornithology. I don't have an issue with it there. Where I do have an issue with it for recreational birding to get the tick/better pictures/better views is that there's no return for the bird at all. It is purely for your gratification, and this seems unsporting to me. However, you have taken the steps to inform yourself and think about the issues, so you would probably use it with some thought.
What I do hate about playback is where it will go. Responsible use giving due respect for the birds and your fellow birders would be okay. It would be a real shame if our bird reserves start to echo with birdsong - most of it emanating from the species Homo ipodus.
I write from a UK perspective where reserves are relatively few and quite small and birders are many, so this will lead to a bad situation in the UK very quickly. I guess if your reserves are large and/or your birders are few the problems are less likely to show for a while and the birds may be able to move away from the noise. In which case you may be okay. At least you have looked at other viewpoints before acting