  There is a remarkable formula for the principal specialization of a type A
Schubert polynomial as a weighted sum over reduced words. Taking appropriate
limits transforms this to an identity for the backstable Schubert polynomials
recently introduced by Lam, Lee, and Shimozono. This note identifies some
analogues of the latter formula for principal specializations of Schubert
polynomials in classical types B, C, and D. We also describe some more general
identities for Grothendieck polynomials. As a related application, we derive a
simple proof of a pipe dream formula for involution Grothendieck polynomials.
