And specifically for Texas, the past decade of losing to teams like Baylor, ISU, oSu, KSU, TCU, WVU, has done severe damage to the perception of the program, despite the fact that in many years those teams have been good-to-very good.
If Texas had been losing SEC games to similarly good but not great teams, the perception of the losses and the program, wouldn't be as bad. This phenomenon is one of the key reasons Texas ended up making the move. The "SEC patina" will be positive for the program, even if it's not winning a lot of football games.
I mean, look what it did for the woeful ags in recent years. Their conference win% is almost identical in the SEC, to what it was in the B12. But the perception of all that mediocrity, has been better than the reality, due to playing in the SEC.