I also have that background. Nobody should withdraw from exercising their legal rights out of guilt or emotional blackmail. Otherwise, there's tacit approval to the notion that schools could break Admissions Law 'because only somebody selfish would appeal'. And it's a given that, without this legal protection and right acting as a check and balance, some schools would break the Law.
Take away the reliable income for independent appeals staff ensuring that decisions are legal, take away the imperative for Governors, Heads and Admissions staff to know Admissions Law and follow it in all cases, and you will end up with schools discriminating against children on the basis of things like disability, income, ability, ethnicity and other Protected Characteristics.
It's no different legally than exercising a right to Trial by Jury or having free legal representation upon arrest in Criminal Law - nobody should be dissuaded from having legal representation and denied the opportunity to be tried by a jury of peers because it's more expensive for the Government; just because the legal test is on the Balance of Probabilities, rather than Beyond All Reasonable Doubt, that doesn't mean anybody should eschew their legal rights out of a misplaced sense of 'social responsibility'.
So do appeal, OP. You may be offered a place completely separately to that over the coming weeks as people make decisions to go to other places, or if the consultation period for EHCP establishes that your preferred school is the best place to meet your child's needs - but still appeal. It's your right, it's the right thing to do and I hope that the Panel make the decision that is right for your child.