Everything "works", you still spent money on stats. But the question is not if you gained something for your money, but whether you could've gained more spending it in other ways - that's why most people don't get Nashor's, even though it's cost efficient.

Cost efficiency is not enough, there's also "opportunity cost", which is all the other things you could do with the money.

The aura never went away, it just went from 2% per 1% missing to 1.5%, and now it's back to 2%.

There was always increased mana regen, it was just nerfed a tad.

Interesting concept.
I have nothing against playing swain, using BfT is good for swain. using mana pots is a neat trick.
crystaline flask will save you tons of money in manapots,and gives health.
I still see no reason not to get tear (archangels/muramana are really good)
Chalice is also very helpful.
new prospectors ring also gives very nice mana regen.

I would start with tear/flask and buy ring quickly or vice versa.

It seems like your problem is that you run out of mana too quickly, and your solution is be very against buying any items that would fix your problem? Maybe it is worth gimping your initial fight damage, for the chance to stay in lane for a lot longer, and not lose your point perhaps?

If you're running out of mana, you're better off not wasting a couple hundred gold on mana pots every time you go back in my opinion. After a few trips back you may as well have bought a tear anyway in gold cost (they're not expensive), and you'll be able to upgrade that later.

Also it depends what malzahar you're facing, if you're up against AP Malz, you'll do well to get an early chalice for the MR as well as your ludicrous sustain through his dots. An AD Malz will be harder to itemize against, without gimping your mana regen. Rushing a chainmail for your wooglets, before getting your chalice might be worth it. But honestly, I would still just get the chalice first for the MR that his early game puts out. My first two buys as swain would be a tear and chalice. Farm it up to insane qualities, then upgrade to seraphs and get a BFT and Wooglets. You shouldn't be able to take out a competent Malz (dunno why I'm still using this example?) immediately anyway. Once you both hit 6 you can start going in on him, but before that just push the minions harder than he can and control the health relic.