A lot of myth-making has been created around the Burnley match. Yes, the crowd was loud but it did not tangibly affect the result. We still lost.
The Brighton players played well, because they showed tremendous character, and worked like crazy to cover the extra space. Any team that is reduced to nine men is either going fight or surrender. Thankfully, our players chose the former and it is they that deserve the credit for their performance, not us.
Cheering CMS on did not mean he developed better technique in finishing in front of goal. It is technique, organisation, tactics, man management and having the right blend of players, that will win games, not how loud a home crowd is.
I agree with what you say, but if the crowd can lift the players by even a small amount, then let's do so. A passionate environment can't make a poor player a good one, but can encourage someone to stretch a little further, chase a little harder, and challenge a little stronger. Arsene Wenger always says that most matches are won by inches rather than yards, and we can be an extra inch, but only if more people buy into that viewpoint.
The atmosphere at the Amex (and nearly all all seater stadia TBH) is not great, but given that the average age of someone attending a PL match is 42 perhaps it's not surprising, just a shame.