Please consider the following before you speculate further:
We routinely find out the color (and hence make a spectral measurement, though not a very accurate one) of light without a length measurement. Also the intensity (and hence a field strength measurement).
Instead of looking at data you can have them read to you by automatic equipment for the blind.
Most real measurements of nontrivial complexity (almost all beyond those of simple introductory textbook examples) are only inferences from raw measurements based on , hence have very little to do with the kind of measurements discussed in the context of the Born rule.
For example, first principles distance measurements as done in GPS rely on complicated computations involving general relativity.
Query to test your quantum understanding: Did the wave function collapse
(a) when the signals arrived on which the computations were based,
(b) when the calculation is completed,
(c) when the result has been communicated to the device on your car and was looked at by you?
(d) in none of these cases?
Reading time from a digital clock also meant a lot of inference going on inside the clock before you could look at the display and (is this a length measurement?) deduce from the form of the black and white distribution the current time. Same problem for all digital electronic equipment.
Measurements such as that of a particle lifetime, a reaction rate, or the
integral cross section of a particular reaction do not even have a natural associated operator of which the measurement result would be an eigenvalue.
The idealized textbook measurement theory based on Born's rule is
appropriate only for the measurement of spin and related variables
that result in recording decisions between a small number of cases.
The measurement process as described by von Neumann (and copied
from there to numerous textbooks) is an unrealistic idealization
compared with many (and probably most) real measurements.
The latter are usually much better described by suitable POVMs
(positive operator valued measures) rather than by Born's rule,
which corresponds to PVMs (projection-valued measures), a special case
of POVMs in which the positive operators are in fact projections.
And no, measurements in general do not cause any collapse,
but the dissipative processes happen all the time, and measuring something means taking mental or automatic notice of something that has been completed and already existed as a fairly stable record in the detector. A record of something that happens to be stable in the detector, not necessarily a length. (In electronic equipment, typically, the stable things are magnetic or ooptical states.)