> Why does a client need to specify an interpreter to run on the master host?
Some system have Python installed in a rather uncommon location. For example, Python is not part of FreeBSD base system, so Python is installed at /usr/local/bin/python instead of the expected /usr/bin/python, or Arch has Python 2 installed at /usr/bin/python2 rather than /usr/bin/python.
Note that Ansible doesn't require itself to be installed on the remote host (and IMHO is one of its biggest selling point) and execute tasks by sending a packed version of a task to the remote host and execute it using `ansible_python_interpreter` (e.g. `/usr/bin/python /tmp/ansible-tmp-a43bf412.py`)