We have setup chroots for SSH access for managing WordPress sites, I posted here about this here, this is fine for most the small sites we host and with around 30 sites per 12GB RAM virtual server it means there are the resources to cope with most traffic spikes and to prevent sites impacting on others we have mpm-itk set to limit the maximum number of Apache processes per site and this mod also allows Apache to run as the user which solves security and privacy issues with shared hosting and Apache running as one user (www-data or nobody).
At some point in the future a Docker approach might be an option and although managing all the WordPress code in git makes sense for clients with a decent budget I don’t think it does for most of our clients as they manage the themes, plugins and updates themselves. (Also they need Apache rather than Niginx so that the .htaccess files work, but perhaps a reverse Ngnix proxy in front of Apache would be good to add to the mix someday.)
Sounds like it could be fun and productive 