The thing is much more deeper than what you described. You need to choose which variables you will assign, that's first. Then you have to assign them, and it is important to do as carefully because assignment may produce inbalanced search space.
Splitting on one variable when there are hundredths of thousands of them is very, very inefficient.
[1] https://www.cs.utexas.edu/~marijn/publications/cube.pdf
The thing is much more deeper than what you described. You need to choose which variables you will assign, that's first. Then you have to assign them, and it is important to do as carefully because assignment may produce inbalanced search space.
Splitting on one variable when there are hundredths of thousands of them is very, very inefficient.