A working transducer should maintain the correct output voltage regardless of the load impedance, so long as it is not overloaded. That's what instruments do.
No. An instrument's voltage output puts out a voltage and expects that what it connects to will not load the output/input circuit. Loading the circuit would create an error of some magnitude.
A voltage output is supposed to be a low impedance output. What it connects to creates two resistances in parallel. The higher the resistance of the voltage input, the less impact it has on the total circuit resistance.
But a voltage output can be 'loaded down' by connection to a relatively low impedance voltage input, with a resulting low reading error.
Those who lived through the days of analog volt meters learned that the meter's coil 'loaded' a circuit.
Most voltage inputs nowadays are at least 1M ohm if not greater, which usually does not load a transducer/transmitter output. A pH probe is a high impedance output, and requires a better-than-average high impedance input to get a pH signal that isn't measured with error due to loading.
A current loop has some ability to correct for resistance in a circuit, like you suggest, "maintain the correct output". A current loop output will change its output to adjust for load changes, within the ability of the loop power supply to drive the desired current through the loop resistance.
Some years ago, there was a thread here involving a level transmitter stopped reading at about 75% of scale and would go into initialization mode. It turned out that the resistance of the mile of copper wire between the transmitter and the receiver/power supply was high enough to let the loop operate below 16mA (75% of the 4-20mA span) but the power supply could not push more than 16mA through the loop resistance.
A current loop driver monitors the loop current and adjusts it to the correct value, adjusting for the loop resistance.
A transmitter's voltage output is not 'adjusted' by monitoring the output circuit, it is created according to whatever its measured process variable is.
Dan