If you set it up manually each time, sure, that won't work very well. But you should be able to automate that - create the config (CA and everything) once and then just spin up a droplet via the API, install the packages, copy and unpack the config. I don't think you'd need to customize more than the sever's IP address in the config.

I built something similar with sshuttle (way easier than OpenVPN) two years ago, it's at https://github.com/lorenzhs/instavpn but it uses the old DO API and is rather hacky. sshuttle also isn't very good for streaming.