I don't think so. NPM packages aren't installed globally by default, they're scoped to the local project via `node_modules`. So by default, the version of npm on the user's PATH wouldn't get updated.
The majority of npm based installation instructions I encounter "out there" are using "npm install -g".
Well, that would be up to the user to decide. And you don't generally install project deps that way beyond some dev-deps like linters and test runners.
Even that guidance has changed with the cultural acceptance of `npx`. At this point the only thing that should be `npm install -g` is npm itself, and that only depending on your philosophy of how current you need to keep npm versus the version that ships with your NodeJS install.
Everyone installs npm globally, because the whole model is broken. Which is why we keep all node env in a Docker image.