Why are certain function calls termed "illegal invocations" in JavaScript?

It's because you've lost the "context" of the function.

When you call:

document.querySelectorAll()

the context of the function is document, and will be accessible as this by the implementation of that method.

When you just call q there's no longer a context - it's the "global" window object instead.

The implementation of querySelectorAll tries to use this but it's no longer a DOM element, it's a Window object. The implementation tries to call some method of a DOM element that doesn't exist on a Window object and the interpreter unsurprisingly calls foul.

To resolve this, use .bind in newer versions of Javascript:

var q = document.querySelectorAll.bind(document);

which will ensure that all subsequent invocations of q have the right context. If you haven't got .bind, use this:

function q() {
    return document.querySelectorAll.apply(document, arguments);
}