The main motivation for modeling p(tls ) in terms of p(wlhi , s) is that it simplifies the "decoding" problem of finding the most likely target text.
if hi is known, finding the best word at the current position requires only a straightforward search through the target 1This ignores the issue of normalization over target texts of all possible lengths, which can be easily enforced when desired by using a stop token or a prior distribution over lengths.