I liked writing chef, but the client/server model and its knock on effects (IIRC, needing to upload changes with knife?) was annoying. Ansible is more painful to write but a delight to run.
In fact every time I’ve migrated to Ansible (each time from Puppet), we’ve built the infrastructure so Ansible pulled its configuration.
A systemd service runs ansible-pull about 2 minutes after boot. It does its thing.
It has some annoyances, but it works fine. I don't think about it anymore. The git repo is the source of truth.
SSH is inadequate because this process should be much slower than the life of anyone's terminal window. You could approximate it with cronjob pulls if each node's schedule is a little offset from the previous. But you probably also want different rollout schedules available for different scenarios.
It also has tons of advantages, notably around scale (Ansible id very slow when working with thousands of machines) and ensuring that there is no drift. Also e.g. SaltStack (RIP) has cool features such as reactor to react to events on the machine which are only possible because there's an agent
I use Ansible personally when I'm dealing with a server or two. I use Puppet professionally when I am dealing with tens of thousands of servers and trying to keep them all in some kind of unity.