That's not how mana works for anybody, except Singed and Ryze.
Mana is a gate resource, AP is a scaling resource. You buy mana items either to have more resource to throw around in fights (common for tanks to get Frozen Heart or Iceborn Gauntlet), but also because most of those items have other effects (FH attack speed reduction, Iceborn slow fields). Resourceless champions aren't supposed to benefit from it; because they're investing gold into an item that grants a resource they don't have. You CAN buy these items for their passives, but if you are manaless, then you won't get full use out of it, and this is fair; you don't have a resource to begin with. If you want to dip into these items, accept that you won't use the gold you sunk into their mana costs.
AP is for scaling on abilities for the champions that have those ratios. Champions who are not primarily AP will get nothing out of building it; Vayne does not use Deathcap or Luden's well, because she doesn't synergize with it at all. At best, these champs will get Zhonya's to cheese an assassin, or maybe a Liandry's in special cases (Mundo). AP is not a gate; mana is.
A champion who has no resource and invests into Sheen will still take advantage of both the CDR and the spellblade. They are able to use it efficiently, but not as efficiently as someone who has mana. A champion with no AP ratios will get much less out of sinking gold into AP items because they can do nothing with the offensive stats provided.