There seems to be 4 main branches of the alchemists powers: bombs, poisons, elixirs, and spells. There are also 4 classical elements. Maybe the alchemist could be re-made so there are essentially 4 different types of alchemist, depending on which aspect the individual alchemist selects.
I also think the elixirs should be more like a binder's vestiges, each providing a suite of related powers and abilities. Some might make the alchemist big and strong, some quick and graceful, some tough and hardy, some smart and psychic, some wise and perceptive, and some suave and seductive.
Sounds like your suggesting what's basically a rewrite to introduce more items to try and balance the class around.
And doesn't the alchemist only get like one Elixir through discoveries? I don't really see that as being a huge class feature for them. I think you might be referring to Mutagens though in that case what you're saying makes a bit more sense. Except right now you can make Mutagens that effect all your physical stats just like you describe, just not the mental ones.
I am assuming by elixers you mean mutigens? elixers are magic items... so it is confusing... and by spells you mean extractions?...