I'll just get the most obvious gripe out of the way: censorship. Thankfully, they're finally starting to move away from it.

As for your gripe, Quiz of Valkyrie seems to be the only game that doesn't tease the mascot. The prologue starts with Liddy's scenes. Naturally, she's the best mascot.

Lord of Valkyrie's Navi does have scenes, but good luck getting her cards. Not that that's relevant now since Nutaku LoV is dead.

Likewise for Ichigo (or Hametena) in Osawari Island. You needed to throw down $100 for a CHANCE at getting the former, and the latter was buried in the ever-expanding SL gacha pool, which is a crapshoot to get even one of with tickets anyway.

Aigis' Anna is an anniversary event that we have yet to get. No telling when they'll ever get around to releasing it.

Dunno about Girls Kingdom's Salome or any of the other card games. I'm pretty sure Nazuna in Flower Knight Girls doesn't have scenes though. I don't suppose Airu in Pero gets more scenes outside of the first stage either.