It’s probably significant that this line is spoken by a character called “Gentleman.” It is often played by a servant character of Horatio – but I think the Gentleman is on purpose. Only a gentleman might find the strength and have permission to speak to the Queen this way. A servant would likely not dare to advocate for the crazy woman outside the door. A servant might be like, “Uh. The Queen says no. Get that crazy lady out of here, pronto.”
Similarly, it’s a little weird when directors have Horatio speak these lines. It makes him seem a little presumptuous and familiar with his friend’s mother – when everything Horatio actually does and says is much more measured – with a kind of distance, a remove from the whole experience. He has a foreigner’s reserve – so to have him plead Ophelia’s case is weird.
This line is a Gentleman’s job.