Mordekaiser is literally the worst support in the entire game. His harass makes him lose life!
But he wins trades via shield.
They might ragequit because they think that they need a support that can better defend them or can otherwise bolster their own power. That's why I suggested Lux and GP. Lux has a decent amount of early game burst assuming you land Q and an auto. GP pokes well and can get some gold from that mastery in the support tree. GP can also transition into a late-game monster if necessary.
Nasus is the suggested pairing there, though, and he doesn't need defense or power. He just needs someone who does damage and can help win 2v3s when jungler ganks (ghost OP). Nasus has all the mobility-removal and damage-reduction power via Wither that he needs. Morde ghost makes dragons and towers disappear.
If inflaton turns $3 into $0, then $6 turns into $3. -Orca