The main reason for not putting it on the G-reg is that you have an FAA PPL on which you want to fly it, not a JAA PPL. And this mostly happens with people who want to have an IR, and don't want to go through the incredible classroom/theory requirements of a JAA IR. So they get an FAA PPL/IR and fly an N-reg in Europe.
Another reason is that the FAA is more lenient to modifications of aircraft than the JAA/CAA. Certain modifications are easily recognised/accepted by the FAA, but require some serious amount of certification work (with the associated cost) before they're acceptable to the CAA. And without that, no CofA and no flying. Even a replacement (brighter) landing light will cost several hundreds of pounds in paperwork, so I heard.
Other than that, there's no reason that I know of. In fact, N-regs are more limited than G-regs, for instance because you can't, for all practical purposes, hire them out to schools or clubs, and you might have to jump through some hoops to get customs and the FAA happy. Also, N-regs are supposed to be owned by US citizens, corporations or trusts, so you will have to set up a trust in the US to own your aircraft.
IO540 has done this and can tell you a lot about the process.