PP Declined - Overly Dominant Extension Vs Local Plan policy - Appeal?

Planning laws are deliberately broad and vague as they allow planning departments to pass or fail anything where they get to make the decision regardless of the actual merits. With the LHES, the government should have stuck to their guns and excluded planning inspectors from the decision making process. Having said that, the LHES itself is poorly drafted and it's quite easy to see how an extension built to maximum permitted dimensions could make a neighbour's life a misery. With my local authority, you've basically ended up with a coin toss. No neighbour complains, happy days no matter how overbearing. Any neighbour complains, the inspectors get to decide and they will reject the application out of hand.

With regards to your situation, it's worth an appeal as it's free and the process itself is actually pretty good. The bad part is that inspectors rarely go against subjective opinions of their colleagues in the local authority. They will tend to dismiss other examples given by saying that beyond the dimensions, no other info was provided. Anything particularly salient in your case, they will just ignore in their final conclusion as they get to pick the points that are relevant. Impacted neighbour did not complain? Well a future resident could! Basically, it's stacked against the average homeowner. And given the final decision is also legally binding, there is nothing you can do about it.

Sorry for being so negative, but that was my experience having gone through the process. I am not saying it's pointless, there is a probability it could go your way, but basically don't get your hopes up. Where it is worthwhile is on technical points of contention. On those you could get clarification or a comment in your favour. Therefore if you do lose and have to resubmit, you know what bits of the design you should concentrate on. Good luck!