Nor should they if they have designs on making the playoffs. Schedule strength isn’t rewarded. People/pundits/poll voters will remember the bad loss to a lower level team, not where the game was played, so why play it at a location that increases the chances of losing?
You’re also assuming that GT has pursued such home and home games with “name” programs. I don’t get the sense that they are.
I disagree about schedule strength. It is remembered – but it's not usually relevant because what matters first and foremost is losses. The four P5 teams with the fewest losses have the inside track at the CFP every year. When teams have similar resumes, OOC competition will certainly be relevant. The problem is that you've got to beat those tough OOC teams before the merits of the victory are relevant. And beating a strong OOC is a lot harder than beating a G5 team.
There have been multiple reports by GTAA personnel, in response to complaints from fans that we're playing the MTSU's and Tulane's of the world, that they have tried to find better match-ups. Back when DRad was in charge we went on that spell of scheduling SEC teams – we actually played Vandy and Miss St several times, and we also scheduled Bama and Ole Miss, until either they or we backed out.
The reason is because no coaches want to play tough OOC teams if they can avoid it. CPJ sees the annual UGA game as an albatross around his neck. He's focused on winning the ACC and having the best possible resume to get in the CFP. Playing one strong OOC team per year is already plenty as far as he's concerned.
The GTAA, on the other hand, is trying to sell tickets and generate enthusiasm. As far as they're concerned, it's their job to schedule the games and Paul's to win them. And so the tug of war inside the GTAA continues, between those who see primarily the benefits of playing tougher OOC teams, and those who primarily the drawbacks.
My primary point to you was that just as you don't want to play the lower tier G5 or FCS teams, the elites don't want to play us.