Your implication of how Ludicrous mode works on the Model S/X is incorrect.This post-drive live stream clearly mentioned absence of any Ludicrous mode.
Which is nice: no need to plan or stage anything. Just go, fast. Am sure that partly takes away the anticipation building up as you put on a production for your passengers of enabling Ludicrous or Insane modes.
But frankly, getting full performance whenever you need/want it is better. This is just a car, and it just works.
Ludicrous mode is, and has always been for public firmware, an "always on" setting for cars that support it. I set my P85D to Insane mode at purchase, and later to Ludicrous mode after upgrade. I set my P100D to Ludicrous mode at purchase. Generally speaking, those vehicles are always in that mode. I say "generally" because I have toggled it on/off for a variety of reasons (different drivers, experiments, etc.) but Insane/Ludicrous was/is my default driving mode.
The "stage" features you're referring to are Max Battery mode, Ludicrous+, and Launch Mode. The first two (MB, L+) are "for this drive session" features you have to enable and usually require some time for battery preparation (temperature). The third (LM) is literally a "staging" activity where you have to manipulate the pedals in a certain sequence and have a limited time to "activate" once the pedal dance is done.
Lastly, and somewhat related, Elon did say Model 3 will have Ludicrous mode long ago (years ago?). Given that the published spec is 3.5s 0-60, I'm willing to "give him a pass" and say "he really meant it will be ludicrous-the-adjective but he's reserving Ludicrous branding for Model S/X." But, technically, he did say -- literally -- it will have Ludicrous mode. If he stays true to the letter of what he said, there may be more to come for Model 3 in this arena.