That's why I don't go along with the "we want to eliminate GA" motive. I can fully see the reason for thinking that, but there must be a motive.
I can well believe that nobody particularly wants to eliminate GA. I suspect that GA simply isn't on their radar. Though I fear that if GA gets killed as 'collateral damage' while trying to achieve something else for "proper aviation" (ie airlines) then they won't lose any sleep nor get too upset over it.
They just don't see GA as we don't speak with a loud and clear voice. The airlines do speak with a loud and clear voice, and pay for a lot of the bills.