Yes, you need to get the right version of Node, just like you need the right version of Python. I've had both largely just work with directions of "Version Y.X", where Y is defined. I've also had the occasion where it still broke with a specific version where both Y and X were defined.
In general, if I have the right version of Node (and I agree, I'd prefer package.json to also indicate the version of Node that was used to initialize it), things work when installing from package.json. Things also generally just work with Python if I have the right major version of Python, and an environment file. My issue is more that the 'simple' steps a lot of people do when creating Python projects -don't- use an environment. They just use whatever is installed globally on their computer, and they pip install any dependencies, then write a readme to pip install things with, rather than lock it down with a virtual environment.