I don´t own a Model S with ludicrous anymore. But when I did, some days I left it in ludi mode but mostly sport because it was already plenty fast and don´t get to punch it that often because of the speed limits. So I would say go for 100D, even tho the ludicrous is pretty nice to have but only if money is not an issue as the price difference is noticeable.
I have P90DL and drive in Lude all the time. I love it. It never gets old for me. However, as WattMobile quite rightly points out you pay a premium for it. Probably depends on your personality and how much of a kick you get from launching. For me it's worth it - not so my wife who drives in Chill.
Whenever I get the chance to drive a P, I use ludicrous all the time. That's what it's there for, and that's what I'm paying for. It does not matter what the weather is, traction control and responsible driving takes care of that. Also, it makes sure you don't get left without options in various situations where a quick speed up helps by adding more safety margin (merges, passing, etc.).
Always ludi, when there is no snow.
When in sport It would be nice to be able to kick through to ludi if needed; like “full military power”. Most issues are avoided by braking, but fast acceleration is a great tool in some circumstances.
Always in ludicrous mode. Gentle acceleration is no easier in Sport or Chill, so I see no reason not to be in ludicrous unless a valet has the car.
The original question might also ask how often we actually use ludicrous acceleration. I do a fair bit, but almost never from a standing start. With practice you can quickly roll on power from low speed, have the accelerator briefly floored and then roll it off smoothly and hit a target speed to within an MPH or two without overshooting. Lots of fun.