Checks out. Honestly, I expect people would generally be more excited for the class if extracting elements was usable on a wider variety of targets - for example if they got a feat for each element to expand the variety - being that bleed get water, beings that breathe get air, plant type get wood, beings wielding metal get metal, casters get fire, etc.
I have dabbled with designing Kineticists repeatedly and even played some a bit.
How are people fitting in Impulses in any builds that feel good? Besides the starting impulses and the flexible impulses you get for free, they feel *incredibly* heavy to pick for me. I already have such a tight feat budget, and especially for the single-gate needing to buy the later impulses manually feels like a huge strain for me and my options - as in theory I am supposed to be good at this, but getting even half my options locks me out of any multi-classing at all it seems.
Some notes, a basic check indicates you didnt make any mistakes.
It looks to me that, by math as written, the Thaumaturge is losing in total damage as compared to every other Martial listed, or is very close. In those cases it is close, that is because unlisted is a major trait that the Thaumaturge does not have an equivalent to being unused in the comparison.
Dual-slice, power attack, familiar precision damage, all effects that the thaumaturge lacks an equivalent to. Nothing wrong with this, of course, the thaumaturge is then slightly behind all martials with a more more consistency and a bit more of a specialty in one-action strikes. Its a unique sort of damage pattern, but very much within 2e standards.
So, if the class is balanced as a martial, it seems to me that adhering to the martial baselines like this is doing makes a lot of sense.
I dont "love" that 2e has these strong baselines with little deviation, but looking at the math here, its at least a distinct way to go about it, and is well within the norms set by the class. Rather than hitting hard, the damage is because your attacks 'burn' into the foe. Its not haymakers so much as salt on giant snails.
Ultimately, utility effects and disables are very guarded, but accessible to *every single class* as part of that. I am not sure it would make sense to try to rebalance the class towards that given the game's core principles. So, what else is there except damage, and damage expressed in a somewhat unique way?
Better save progression aligns with MAD. High will especially aligns with using CHA to do many things WIS normally does, while still enabling specialists.
Many abilities rely heavily on class DC, like the Wand, therefore higher class DC is consistent. If anything, I feel it is weak enough that one will have *trouble* relying on things like the wand usefully. This seems to be a common perception as I have seen *0* playtest reports using the wand.
Amulet Reaction only works against your EA target, therefore is more restricted and generally weaker than you rate it. Playtest data supports that it gets considerably less use than champion reactions.
Warding Circle is a place of safety or a prison, or just a wall. Circles have powerful thematic significance, and it can fill many purposes as it prevents movement both ways.