Sending keyboard events programmatically doesn't dispatch them into inputs

I am sending programmatically generated keyboard events to the document. I was hoping that the currently focused input element would display them, however it doesn't. The events are generated from a string with this function:

const simulateKeyPress = keys => {
  keys.split('').forEach(theKey => {
    const e = new window.KeyboardEvent('keypress', {
      bubbles: true,
      key: theKey,
      keyCode: theKey.charCodeAt(0),
      charCode: theKey.charCodeAt(0),
    })
    document.dispatchEvent(e)
  })
}

If I add an EventListener to the document it'll receive all the events. Their isTrusted flag is set to false however, might this be the issue?