To give some scale to the topic: Measured values with a ZRA are typically 5 to 25 uA DC. The ZRAs I used would run for about 90 minutes on 2 AA batteries (that's three months at six-hour awakening intervals), so yes, they are power-pigs.
ZRAs are used in corrosion, and I can't see why they aren't used in micro-current DC electronics. DMMs inject current and voltage for other measurements, why not inject current to measure current?
I don't recall the term TIA (I did read the references provided above), and I don't recall the circuit of the devices I installed.