It's not the only possible way to do things, and sometimes it's infeasible, but it definitely makes things simpler. In theory if you have N quantities, and N measurements that all depend on all N of those quantities in known but different ways, you can usually compute the N quantities precisely from the N measurements.

For example, the standard way to make an electronic thermometer is by, more or less, measuring the current across a semiconductor diode at a given voltage. This current is an exponential function of the ratio between the voltage and a "threshold voltage" or "thermal voltage" Vt multiplied by an "ideality factor" n: I = Is (exp(V/(nVt)) - 1).

The threshold voltage Vt varies linearly with temperature (it's kT/q, depending only on Boltzmann's constant and the charge of the electron, about 25 mV at room temperature), so in a sense the current at a given voltage is a measurement of the temperature. But the ideality factor n depends on the purity of the semiconductor material (generally in the range 1.0 to 2.0), and the saturation current Is depends on the physical size of the diode junction. Moreover, the ideality factor can change over time as the diode ages. So we're in the position of simultaneously measuring the temperature, the size of the diode, and the quality of its aged semiconductor material.

The solution usually taken, as I understand it, is to measure the current through the same diode at two given voltages, one after the other, and to use a standard value for n which is good enough. Then the ratio of the two voltages tells you nVt (as long as the "- 1" is too small to matter) and from that you can calculate the temperature. In theory, by taking three or more measurements at different points in the I-V curve, you could correct for unknown n as well, but I haven't read of anyone doing this; instead, for high-precision thermometry, they use an RTD.

(Actually, you measure the voltage at two given currents, because that way you don't burn up your temperature sensing diode if the temperature is a little higher than you expected; the power dissipated then varies logarithmically with temperature rather than exponentially. But it comes to the same thing in the calculations.)

It's actually even worse than it sounds, because in fact when you measure a voltage, you're always measuring it with respect to some reference voltage, so your actual measurement is a function of the temperature, the saturation current Is, the ideality factor n, and your reference voltage Vref, which is typically subject to an error of around 2%. But you will note that the ratiometric approach described above cancels out any errors due to Vref, because the ratio of the two voltages will be unaffected by a wrong reference voltage, as long as it's the same wrong reference voltage. So you stick a big capacitor on it and take the measurements in quick succession.

All of this is, from a certain point of view, in the service of making the number you finally produce very sensitive to the temperature of the diode and very insensitive to other factors, like the battery voltage, the temperature of the rest of the thermometer circuit, the age of the components, the humidity in the air, and so on. But all of the actual physical quantities being measured on the diode are the complex mix of factors described above.

MIMO antennas or phased-array receiver antennas or microphones are another example: the signal at each antenna/microphone is a linear superposition of all the differently-phase-shifted source signals, and you process that data to get independent measurements of all the original source signals.

I wouldn't be surprised if chaotic metrology offered new ways to measure very tiny differences, but I suspect it will take a lot of time to figure out the math to make that work.