In real life I observe that the classical saturated drain
characteristic is an academic fantasy, and there's a lot
of "curl" to the ID-VD curve. Making Rout reduce, and
there goes your gain. SOI kink effects are even worse.
Even in a well behaved technology that hasn't been
"optimized" to the bone, leakage vs reliability vs speed,
higher Vds shortens your channel and will lower Rout,
while you are also perhaps forced away from peak gm
current densities (for that drain operating point - peak
gm position varies).