Now as integrity is a stake for the GPS, then it cannot be certified as sole mean but as PRIMARY mean of navigation.
Quite incorrect, for ops in the USA or for US registered aircraft, worldwide.
WAAS certified GPS navigators can (and are being) installed in aircraft as a
sole means of navigation, and are fully certified as such.
Don't need VOR.
Don't need ADF.
Don't need DME/TACAN.
WAAS/GPS only, if you so desire.
Of course, others trail behind, which is no surprise...