Don't kid yourself - nothing is gonna change day to day as far as fanfic is concerned. You'll still have all the same fanfic sites.
If, and it's a whopping big if, Star Trek ever gets included in Amazon's master plan, you'll just end up with three levels of Star Trek author rather than the two you've got now - amateur and professional. A new category slips in between those two that combines a little from column A and a little from column B - an amateur Star Trek writer who gets paid a little for their work.
As for why people will pay for fan-fiction when it's abundantly available online, the answer is easy - the vast majority of fan fiction, whether it's Star Trek or whatever else, is complete shit.
Official Star Trek books are ultimately fanfic like everything else, but fanfic that has been edited multiple times to increase the quality.
Amazon are gonna check the fanfic it puts up to make sure it's legal, family-friendly, legible and has at least some level of literacy to it, again unlike most fanfic that is put onto the internet.
If people who are already writing this stuff can make a quick buck from it then more power to them, cos don't pretend you have any ownership over the stuff now whatever characters you create.