Sadly the F-35 is failing in this latter role. At a recent air show in the UK it was the elderly Ukrainian Sukhoi machines that got the gasps of oohs and aahs from the crowd. The crowd were not what you might call communist, they just know what planes put on the best show.
There are no figures bandied around regarding the PR value of the F-35. Facts don't come into it when emotions are involved and the F-35 is fundamentally not loved or held in awe. Plenty of times the USAF have had planes that amaze everyone's inner 9 year old, the F-35 just doesn't cut it.
Meanwhile, in Russia, lots of people take pride in their war planes and believe them to be the best in the world. It could be argued with fact things that their planes are rubbish but facts have nothing to do with belief.
Ultimately it comes down to the air show, not what the pilots say, whether they are paid shills or not. And nope, there is no use for a 'Cobra manoeuvre' but the crowds lap it up, think their pilots are aces and let their kids join the armed forces on that basis.