This is an example of poor game design that Riot is guilty of when it comes to perks of a champion, and there are some examples later. Basically, Riot gives a champion a sort of "advantage" unique to that champion. Sion endlessly stacks health, Thresh stacks AP and armor, Lissandra gets free spells, Orianna's basic attack etc.
So, the idea is "I'm gonna have a shit ton of health as Sion" or "A shit ton of armor as Thresh" or "A shit ton of mana as Lissandra." or "I'm gonna have high auto damage as Orianna".
And you are correct in that assumption. That's how it should be. That's the point of the champion, and partly why you pick them and why they incorporated that mechanic in their kit.
However. Riot implements a counter measure to these boons that serve to not really put your champion ahead ever. Sion has the lowest base health in the game. So sure, you stack health per creep but at 18 your max health is only like 1600 or so. Notice what Riot did there. So the amount of creeps you need to kill to contend with other champions at a base level is absurd and some of the higher end ones can't even be achieved. It's a mechanic in Sion's kit that makes you feel big, but was nerfed in terms of base stats by Riot.
Same with Thresh. Each soul gives armor, woo! Tanky thresh! Except...he has no armor gain unlike all other champs. So, his armor is actually..about the same. It's dumb and nonsensical and just bad design. Riot couldn't think of a legitimate passive so they give him a stacking passive that seems unique but they nerf him so that it really doesn't do anything.
Same with Lissandra. Sure you have a passive that lets you cast free spells here and there. So you'd expect your mana should hold out better than other champions. Wrong. Your mana regen is slashed to keep you "Even". So you are basically a champion with 4 spells and half a passive.
Orianna has her passive that augments auto damage. Scales with AP. So you assume "Hey, I'll have an advantage in CSing and auto trading with my laner because mine are stronger. right?" Wrong. Base AD slashed down to what I believe is either 40 or 41.
Galio used to be a victim to this but they realized he was useless and fixed it. His whole basis is being an MR tank. He acquires AP off of MR. So you're thinking, "I'll have lots of MR and be an effective MR tank and have some good AP to boot." Wrong. He had no MR per level. Another nerf to the base champion to somehow justify the kit they gave him. But, after nerfing his core item Athene's, they gave him 1.2 MR per level I think.
I'm surprised champions like Nasus don't start with like 10 AD, or Veigar doesn't get 80% effectiveness from building AP items. It's a poor design to incorporate a strength into a kit and justify it by nerfing the base champion.