Doing puzzles blindfold with a few pieces helps you to visualize and understand the chess board. You realize there are static relationships between the squares.
You can build your intuitive understanding of the squares to know things like:
The e4 square is always a knight's move away from f2 and g3. The e4 square is light and the f2 and g3 squares are dark.
The f2 square is diagonal to g3 and those are dark squares (a light-squared bishop would never interact with them).
The f2 square "has opposition" with the h2 square (a king on f2 prevents a king on h2 to going to the g-file)
And so forth
You don't have to see the entire board in your head, simply realize there are static relationships between the squares. The squares have an impact on other squares around them.
Blindfold can also make a "simple puzzle" more challenging, and just like a bodybuilder or athlete, you need to challenge yourself in order to improve and build your (brain) muscle.
Why endgames?
Doing endgame puzzles and studying endgames is great for improving your calculation abilities. Endgames in general help you to understand chess. There is an old adage that studying openings helps you with openings, but studying endgames helps you with chess, in all phases of the game.
If you learn an opening and your opponent deviates from the line you know, you're probably back to square one. But when you learn endgames, those specific positions might not come up in your own games, but the concepts and techniques you learn will come up time and time again.
