I'd argue that the damage has already been done with Skype and other online meeting tools now meaning that people generally - to some extent at least - don't have to fly for business any more and those choosing to (I'm one of them) will reduce in number over the next 20 years to the point where business travel will be a curio and nothing more.
Flight shaming will only make this process faster.
Bear in mind its not as if we as a business community are facing a lot of pushback from our companies in terms of pushing us to fly more for business and us execs are trying to reduce it etc. The opposite is true. I work/have worked for energy/oil companies who are allergic to spending money. People in my industry used to fly a lot and in premium classes. Now the premium class travel has gone even for long haul and the economy flight budgets are being pushed back and back as its cheaper to send an email and hold a VC. We used to go to all the seminars and conferences, not any more. Flight shaming and the environment has been a useful excuse for many employers to cut budgets back massively. Its low hanging fruit when your shareholders only care about your bottom line profitability as you can make excuses about revenue growth or lack of it.
Its clever in a way as my company will fly me AMS-IAH or AMS-SIN or AMS-PVG only after I get several signoffs from management, complete endless forms and declarations etc all designed to push me toward the video conference route. And if I get the green light I'll only be able to fly cheapest economy and only then if I fly on my weekend and not during company time. I cant even go non-stop very often - if its cheaper to go one-stop then that's what they'll book. If I want a flex ticket, checked bags etc I have to pay for it.
I wouldn't fly AMS-IAH/PVG/SIN etc in economy if I was doing it for personal reasons but I have to if I'm doing it for a multi billion dollar energy company. Its a long flight and its a waste of my weekend so I cant be bothered. VC all the way now, its not worth the effort and dramas to try to fly. Of course that's why it is how it is - to stop you from asking and push you toward the VC.
The environment is just an excuse!
Well, there always will be a lot of us who actually have to go to the customer to do hands-on work. And to get to the customer will often require flying. But hey, if the flight "shamers" are willing to pay for my time while I'm traveling across Canada by train, I'm willing to do it.