But you can declaratively specify a full system configuration in a real programming language, too. This is precisely what the GNU Guix system configuration API does, for example. You write OS configs in functional, declarative Scheme code.
http://www.gnu.org/software/guix/manual/html_node/System-Con...
This is the real reason.
The playbook is the final state. How it gets there is of no interest to you. All you need to be concerned with is the final result - the state described by the playbook. All the extra complexity is handled by the software.