As an architectural historian, I recall a couple of small archaeological
investigations that I thought were wasteful, even stupid - simply because
their purpose was to determine the date of extant houses that could be dated
to a very narrow time frame on the cheaper, simpler, and less invasive method
of analysis of the stylistic and construction evidence of the building.
  These were rather easily dated mid- to late-18thC. buildings (no thanks to
documentary evidence, which was sorely lacking) and the archaeological
investigations only provided a much broader time frame of initial
construction than a competent architectural historian might have concluded in
a half-hour's work.
 
These rare and ridiculous examples aside, I'd argue that historical
archaeology is absolutely and frequently of great importance, even, and
sometimes especially, on sites where reams of documentary evidence abounds.