To play devil's advocate for a bit: there's a bunch of spells you probably want to learn anyway, ATK is also a pretty massive money sink, the Slime can be built as a pretty strong melee attacker and Defensive Stance does not reduce MATK so mage Aura tends to be a pretty tanky Aura against physical fighters.
I think the game is trying to be balanced around the idea of your Slime filling the role Aura isn't filling. Dueling becomes an absolute pain on mage runs though.
At to the optimal use question:
Probably best to either sell the living hearts or feed them to the Slime(materials fed to the slime give EXP based on their gold value) with selling winning out as far as I'm concerned. DEF/MDEF/Resistances tend to matter more for survivability than HP since good fights are the ones where you can stat-check hits into single digit damage and honest hard work at the blacksmith(or drugs if you need them) is a better way to bump Aura's HP. Pyromantium and Ether are best saved for when you unlock Verdeaux since their stat gains aren't great and the workshop gets more expensive every time you enhance equipment.