Is it obligatory to wish for all people to believe and enter Paradise, even though Allah has informed us that this will not be?

There is a distinction between Allah's religious legislative will (al-iradah ash-shar'iyyah ad-diniyyah) and His cosmic preordaining will (al-iradah al-kawniyyah al-qadariyyah). The cosmic will occurs whether Allah loves it or dislikes it, whereas the legislative will only pertains to what Allah loves, and it may or may not occur. The believer is tasked with conforming to it.

A believer's wish for all people to believe and enter Paradise aligns with Allah's legislative will, and it indicates their love for Allah and His religion, just as the Prophet, peace and blessings be upon him, was eager for this and strived towards it.