I. The only problem in the entire University of Chicago Math Project Algebra involving the division of a multinomial by a polynomial (p. 730):
There are no problems in University of Chicago Math Project Algebra that involve polynomial long division.
II. The first problem set in Wentworth's New School Algebra involving polynomial long division (pp. 70-71) [click to enlarge]:
Polynomial long division provides lots of practice with the distributive law: here, one is constantly distributing both monomials and the negative operator across polynomials. In addition, polynomial long division shows you place value at a more abstract level: here, one can discuss, for example, the c2s and the cs places. It also shows you the long division algorithm playing out at a more abstract level--which I recall finding quite enlightening back when I did polynomial long division (a few decades before Reform Algebra eliminated it).
1. Is there a good reason not to have today's algebra students do lots of polynomial long division?
2. Is there a good reason to wait until p. 730 of an algebra text before doing any binomial by monomial division?