Enterprise languages like Java or C# are often called "bondage and discipline" languages. They make it easy to use static analysers and to write APIs with very strict rules about what is or isn't acceptable use or input. An incompetent programmer can still write bad code in these environments but they are far less likely to cause considerable damage as long as they follow the rules.
Apart from making it easier to limit the damage bad programmers can cause (which is a much bigger problem the larger your company is, especially if it is not a tech product company or if the software is optimized for longevity rather than developer comfort) these languages also often enable a lot of tooling by virtue of being easy to statically analyse.
Dynamic languages like JavaScript (or even Ruby and Python, though slightly less so) are very hard to analyse statically unless you limit yourself to a subset of the language. That is why Google first created Dart as an alternative to JavaScript and then put their weight behind TypeScript (which Microsoft created as a stricter superset of JavaScript with type annotations). Facebook took a similar approach by creating Flow as a static type checker for JavaScript (with their own type annotation syntax).
There's also the matter of integration. For many enterprise corporations a lot of Java/C# code is effectively glue code to tie together software from enterprise vendors like Oracle, SAP or Microsoft. While Microsoft has been opening up and standardizing their APIs recently (e.g. moving from a proprietary undocumented single-sign-on system to OAuth 2) this is mostly part of their effort to evangelize web developers (who mostly moved away from Windows because it was too different from their production environments running Linux).
But in my opinion where Node.js really shines and has seen some acceptance in the enterprise is as a "glue language" to write micro-services in. Building small services to provide specific functionality (e.g. realtime notifications in a web app) is extremely easy in Node compared to, say, enterprise Java, and thus Node is often added to existing stacks rather than replacing them entirely. It may not be suitable as an enterprise general purpose solution but it's great for small off-hand projects that need to be released outside the regular enterprise cycle -- similar to how PHP often ends up in the enterprise.
Great answer! I just wanted to add that Node.js is already used by big companies in production (e.g. Paypal, Netflix, etc.).