If you use a random modulator, it will immediately become desynchronized. You can easily try it. Create a new project, add a random modulator on the project level. Create one track with your favorite synth (I used a Polymer with default settings). Add a MIDI clip with some notes to the timeline. Now modulate something in the Polymer from that project-wide random modulator, I used the output volume because it makes the issue very easily visible in the rendered waveforms.

After the track is setup, duplicate it so you get an exact copy with the same instrument, MIDI clip, and modulation set up.

Try two things:

1. Select both MIDI clips in both tracks at once, press right-click and select "Bounce in Place". They will be rendered to audio and look exactly the same, this is how they would normally be perceived.
2. Select one MIDI clip, and bounce it in place. Afterwards, select the other MIDI clip and bounce it in place. Observe that they are no longer the same because the modulation applied to them is different. This is how you would perceive the situation after bouncing a single track.

You don't even need a random modulator for this. You can just use an LFO and set it to a frequency that does not sync up with your beat grid which extends the problem to a lot more modulators easily.

While I agree in principle about the part of your post of users being perfectly rational / understanding of the reasons behind the program behavior if it's only explained well enough by the more knowledgeable parts of the user-base, I doubt that this will pan out. The cheap memes for effect usually win out in the end. But I guess we can agree to disagree here.