You absolutely can install a G5 in your plane without going through any FAA approval process (other than the IA sign-off). The issue is that you don't want to pay for the version of the G5 that comes with the STC / Approval already done for you. I get it - my flight budget is pretty tight. For some people it might be worth the money, and for others it isn't. Your airplane, your decision – no argument from me there.
But I really cannot see how either the FAA or Garmin are "making flying less safe" because you have chosen not to avail yourself of their offering for your certified airplane. You seem willing to spend $1300 for the experimental G5, but for $900 more, you could have the approved version with the STC.
Yeah, I wish we could use the cheaper experimental version, and no, I'm not spending the $2,200 to put a G5 in my '65 Champion 7ECA either... But I do recognize what a huge step the FAA (and Garmin, for that matter) have taken in getting the STC approval done for the G5 (as well as the Dynon/EAA/FAA partnership on the D10/D100). I've flown less than 50 hours of actual instrument time, but had 3 vacuum pump failures. Being able to purchase a G5 for well under the cost of an AI and Vacuum Pump is a huge win in my book!