I'd take a mage over an assassin for my team, any day

By assassins I mean single target, damage focused assassins like Zed, Nidalee, LeBlanc, Akali, rather than AoE assassins like Katarina, Ahri.

Assassins are really just balls of damage, they don't offer anything to the team other than the possibility of killing their adc. Even then, mages usually outperform asassins in the damage department. Mages such as Vel'koz or Xerath can easily 100-0 a squishy too, from distance, so that mobility isn't even required. On top of that, the damage mages offer are AoE, so they can unleash their burst on potentially 5 people rather than just one. In a teamfight, a well placed Orianna or Vel'koz combo can wipe out the entire enemy team, let alone one squishy carry. Assassins don't have that kind of power.

Mages typically have long range, AoE crowd control, whether it's AoE knockup from Vel'koz or Orianna, AoE stun from Cassiopeia, Syndra and Viktor, or wall from Anivia. Some of them like Orianna and Lux even have shields. Assassins on the other hand, have at best a single target root from LeBlanc, or a weak AoE slow from Zed.

Assassins are literally balls of damage, that often still deal less damage than mages. They often end up leaving your teamcomp wanting more.