Alternative definition of pairs

Louis Reasoner thinks that building a stream of pairs from three parts is unnecessarily complicated. Instead of separating the pair (S₀,T₀) from the rest of the pairs in the first row, he proposes to work with the whole first row, as follows:

(define (pairs s t)
  (interleave
   (stream-map (lambda (x) (list (stream-car s) x))
               t)
   (pairs (stream-cdr s) (stream-cdr t))))

Does this work? Consider what happens if we evaluate (pairs integers integers) using Louis's definition of pairs.