Praise be to Allah.
This question was put to Shaykh Muhammad ibn Saalih al-‘Uthaymeen, may Allaah preserve him, and he answered as follows:
That is not obligatory, because acts of worship are conditional upon a person’s ability to do them. That ability cannot come from someone else. So neither party has to do this for the other. But if the father asks his son who is able to finance his Hajj to do so, the son’s responding to that request will be part of the honouring of one's parents that is enjoined upon children, so it is obligatory in that sense. And Allaah knows best.