Is rapid chess improvement actually possible?

All sorts of writers and course creators offer this as a key motivational selling point (and not just the controversial Michael de la Maza -MdlM). It is attractive. After all, everybody wants to improve quickly. Right?

Obviously it is possible if measured crudely as rating gains in a calendar period. However, that doesn't factor in the starting level or the amount of effort required.

So, MdlM shot up to 2000 pretty quickly but he started from a low level and put in long hours of training consistently. Of course that is is not to suggest that this is bad, rather that you can't expect similar gains if you don't have the necessary pre-conditions (notably, the time to study).

Axel Smith made astonishing progress from 2100 to GM, but how much work was he doing? If you finish all the puzzles in the Woodpecker Method in one day you have clearly developed some study endurance!

But all this begs the question, "should you be striving for rapid improvement in the first place?" 

Perhaps it is better to take a slow but more thorough approach to your learning.

Rapid improvement is improvement that comes from doing the right things, i.e. refrain from doing the wrong things, that slow down your improvement.

Wrong things include:
Playing blitz/bullet
Analysing won games
Study of openings

Some interesting if perhaps controversial points. what do you think would constitute rapid improvement? Obviously this will differ as rating increases,, so at 1500, 1800 and 2000.