This argument is all based on a 1950's use case for an analog scope testing for over modulation of an AM transmitter. It is *so* last century. A DSO should provide a spectrum analysis mode for this use case.
When you see spurious side bands the modulation is too high. Besides, very few people have a need to test the modulation of an AM transmitter in 2020 other than broadcast engineers who will be well equipped for the task
Have Fun!
Reg
AM modulated signal was simplest signal to explain that points to the problem.
Since you seem not to have answer to that, let's try something from this century.
How about switching power supply, 1 MHz switching frequency, responding to a load pulse from zero to max load and back, 200 ms cycle. What would you see on a output mosfet gate?
And list goes on.
You can have a system that uses sensors that gathers some useful signal and some noise, and than massaging data to extract only portion that is interesting to you.. Like crankshaft sensor, where we take some pulses and noise and extract pulses that we count to extract frequency /RPM. Here we try to discard as much of sampled data and keep only data that gains us RPM info.
These are types of system you worked on your whole life, just yours were insanely more complex and sophisticated.
If we connect scope to that sensor, we want to see signal coming from sensor with all of the crap. All of it. No filtering and such. We use scope not to extract RPM data, but to verify sensor signal, including noise level, and we are doing it in time domain, correlating it to other sensor edges etc.. If there is noise, we want to see it all. And correlate sources in time domain, i.e. temporal correlation.
Make note that in this context word noise is used for all spurious and unwanted signal injected into system from any source in addition to wanted signal.
We might want to analyse noise for it's spectra and distribution, if noise is persistent (cannot be temporally correlated to known source) so we might try to find it's source that way. This is where we use histograms and spectrograms and what not. Here, your expertise is pure gold, and these are thing nowadays only high end scopes have,each to different extent. Some less expensive scopes are starting to have histograms, but like FFT, if control is limited, it has very limited usability.
If someone is capable of adding features of high end LeCroy to inexpensive scope I'm all for it.
But you cannot break how scope works. You have to keep what is perfect the way it is and add to it.
I believe few years ago I gave you advice to get yourself a Picoscope. They are perfect for you. They have all hardware things sorted out and nice ready made API. So you just grab a chunk of data and start analysing. You could make software for it that puts LeCroy to shame. Hell, if you would make it good I would pay for it...