Why is reduction mostly associated with proving hardness?
Actually, people do commonly use reductions for both purposes: both for proving lower bounds, and for designing algorithms to handle a certain problem.

For instance, it's very common to reduce a problem to linear programming, to a max-flow problem, or to another well-studied problem.  This is using reductions for solving problems.

Any particular textbook might focus more one or the other use of reductions.  That's a philosophical choice on the part of the author.