Why is anyone quizzing the CAT A departure? In commercial ops it is a requirement not an option. So debating whether a takeoff profile other than this, is better - is a load of Bo**ox.
The pilot initiated a standard departure for the size of the site.
The probable causes now remain:
Part of the TR assembly failed and departed flight.
Something struck the tail area causing a catastrophic failure.
Once an aircraft enters a developed TR failure flight path (rotating) NOTHING the pilot does to recover (with the cyclic) will resolve the issue simply because the pitch/roll datums continuously change [as described earlier very succinctly].
The suggestion that the pilot fought to steer clear of people or property is wishful thinking At this stage in the flight, the pilot(s) became a passenger.