They do build damage. However, they are considered a MAGE, not a mage SUPPORT, if they build absolutely nothing different from the build they would have if they were going into a solo lane.
That's the problem I'm talking about. Even if you're Lux, Karam, or Morgana, if you queued up as Support and built their Mage build instead of any items that could be considered supportive, you lied. You CAN QUEUE UP AS MAGE. That's why you SHOULD NOT put support if you don't play on playing that way.
There is a rule against lying in the queue, it's under refusing to communicate the fact you're not actually a support, but a mage instead.
You may not have to build both a sightstone and a spellthief, but if your build at 20 minutes looks like you're a mid-laner who's feeding because you have no income item, you're NOT a support, and you're not supporting the team in any way. You're a mage who's behind on gold and there's no argument you can make against that, since your build is that of a mage who's behind on gold and not a support.
Final point: If you play FIZZ. You queue up as WHAT YOU'RE GOING TO BUILD. If you put Assassin, you're building damage items. You are not building Sunfire, Deadman's, Visage, and Zz'rot, Runaan's hurricane, and Banner of command. Those are not damage items.
You seem to be under the impression that building AD when your champ scales AP is what I mean. It's not at all. The role you pick is decided by the items you build, not the champion you pick.
If you want to build Assassin Leona, that's all well and good but don't put Tank, since you won't be building tank items.