I think the issue is that mana regen and/or mana aren't budgeted properly for casters. Let's take Malzahar as an example: You want to get Sorc boots and deathcap, of course. You also want to get a void staff eventually, so that's three slots gone. However, you also want to build Liandry's since it provides even more magic pen and the passive is massively powerful. And if you build Liandry, you need to build Rylai. This leaves you with precisely one free slot to change your build around. And this is a build which any DoT intensive mage will use: Malz, Swain, Brand, Cass, Morde, Morg, Rumble, Viktor, etc. Even mages who don't use DoTs will often pick this build because Liandry's is that strong. In fact, it's so strong that mage damage is currently built around having it.
Even skipping Liandry's and Rylai, you're left with three slots. In those three slots, you need to fit AP, cooldown reduction, mana and mana regen and some survivability. That's rarely doable. Like, let's take Karthus. You build Deathcap, sorc boots and void staff. You also build archangel, and zhonya. Pop an abyssal on top. Sounds nice until you realize you built 0 health and 0 cooldown reduction, but in Karthus' case that works because he cares about neither. Doesn't work so well on most other casters.
Now, forcing people to choose could be seen as an intelligent design decision; it prevents you from getting everything with a specific build and forces you to make choices. This would be fine if other characters weren't able to get everything in a build. Let's take Darius, as an example. He uses mana, but he doesn't need to build either mana or mana regen as his ability costs are low enough to allow him to use them consistently past the laning phase. Build Randuin's Omen, Merc Treads, Black Cleaver, Hydra, MoM on him and you have the following stats and effects, not counting movement speed:
- Magic resistance (+65)
- Armor (+70)
- Health (+700)
- AD (+185)
- Lifesteal (+12%)
- Amor penetration (+10, +25% from debuff)
- Cooldown reduction (+10%)
- Tenacity (+35)
- Cleave
- Attack speed slow on opponents.
- AoE slow
- AoE physical damage
- Magic shield
You get plenty of each of those stats and that's with only 5 items, meaning you still get to pick a 6th item to adapt to the match situation while having all the stats you could ever need. And Darius isn't even the most versatile Fighter. You need to face some mages? Get banshee's. Just tankier in general? GA or Warmog. More damage? Bloodthirster. Tankier AND more damage AND a slow on your attacks? Frozen Mallet. Physical damage champions can have their cake and eat it. Mages can't. Hell, for the sake of comparison, let me compare the 5 items Malz build to this:
- AP (340 +30% = 442)
- Magic penetration (30 + 35%)
- Health (+700)
- Bonus damage over time
- Slow when doing magic damage
And that's it. Same amount of health, no armor, no magic resistance, no cooldown reduction, no spell vamp, no tenacity, slightly better penetration. As for comparing the AP to the AD, you know damn well, that 185 bonus AD is about as good as 442 AP. And on top of that, mages need mana and/or mana regen while most other champions can get away with building neither. I'd go so far as to say that the budget on mage items is so bad that if it wasn't for the fact that you need one mage on a team to force the enemy team to build some MR instead of all armor, people would stop playing mages entirely. Or at the very least, they would concentrate on CC heavy mages and build support items.
)
can do without mana.
on PBE instead of improving the horrible 
) are punished for using abilities willy nilly by having low mana regen to start off, and then are forced to get items that help with getting their mana pool back up to a safe level, or even with having a very costly combo, or even high mana costs on their spells.
The manaless champions are mostly AD, so they don't even need the Morello, and the AD item choices are pretty limited because some are just terrible choices, and a lot of the times are more costly than the AP items.
