How am I able to run npm install/nvm install if I haven't already installed Node? I've seen way more machines that come with Python than I've seen machines that come with Node. You need to install and configure nvm, just like you need to install and configure Python.
The difference is that pip comes from a time when package managers were still universally global, while npm and friends only operate on directories by default.
If you want a systemless Python then you'll have to do it manually. I don't think it happens often enough for it to have a tool like nvm. Nothing prevents you from downloading the binaries, stuffing them into your user folder and setting up the right environment variables in your .profile, except for that it's a pain and probably not worth the effort.
Edit: apparently pyenv is a thing. I haven't ever needed it myself, but it seems to do everything nvm does and more.
If you just want to restrict package installs, versions, and configurations to a single project, virtual envs are the way to go.