Using jQuery to listen to keydown event

In practical terms, nothing you have to worry about. The browser is already going to be bubbling that event, and even though it may be trapped by the body and run a selector from the delegated event, this is not a deep or difficult practical check for JQuery to perform, especially with an ID-only selector.

You could still use .on()

$(document).off('keyup#textfield');

$(document).on('keyup#textfield', function(event) {
    if (event.keyCode == 13) {
         console.log('Enter was pressed');
    }
});

If you want to capture the keypress anywhere on the page -

$(document).keypress(function(e) {
  if(e.which == 13) {
    // enter pressed
  }
});

Don't worry about the fact this checks for every keypress, it really isn't putting any significant load on the browser.