2 hours of learning Ansible & I had the same kind of thing working on a legacy app.
This even worked on a shared host with no root access.
Might make more sense to spend effort on a tool that can scale with you.
I didn't knew Ansible. Seems really simple and powerful, indeed. I'll try to use it, for sure.
Ansible needs python at remote site. Sure many distros already have python in default installation. But if python is not available (legacy, old, no-auth?) or you prefer shell scripting, than sh-simple-deployer and cdist are good candidates.
I prefer Ansible but it's not a 2 h tool. Only if I want to print Hello World. Ansible manual is vast and I need a lot of the modules and other concepts (roles, yaml, Jinja, etc) to really say "Wow, this is better/faster than scripting". Maybe a week. :-)
Good point about the python dependency! If you don't have that, it won't work.
But I wasn't exaggerating about the 2 hours to get a useful versioned deploy from Git working. I used the Deploy Helper module as a starting point:
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