You shouldn’t read the Inferno without reading the Purgatorio, at least. Should English-speaking students be required to read the entire Divine Comedy as do their Italian counterparts? No, if they have to read an entire epic, it should be Paradise Lost instead, although the current-day focus on Shakespeare is fine.
Dante is important to Western culture broadly, but he’s far more important to Italy in particular. From what I can tell, Dante is far more important to the modern Italian language than Shakespeare is to modern English. Milton himself wrote in English of course, and while admittedly the language of Paradise Lost is more difficult in general than Shakespeare, it’s not impenetrable to a bright student, nor does it require an antiquarian bent to appreciate as does Spenser. I can’t read Italian, but translations of Dante don’t have the same touch as Milton’s English.
