Could this film work set in modern day.

Not really

No, unfortunately it would not work.

People today do not have a sense of honor, introspection, etiquette nor commitment to familial duty.

It would have to be set in a culture that has stricter social rules and mores than mainstream US culture.

Of course it can. Especially if set in the US. The user above me has written it can work only in a society with restrictive social rules, but, at least from the European point of view (I'm Italian) Americans do have strict social rules. Even so-called liberals in the US are very conformist if compared to Europeans, at least to Western Europeans (Eastern Europe is much more conservative and narrow-minded).

If you want to set it in the western world, it'd have to be the story of someone who belongs to an extremely conservative subculture. Say, make it about a minister who belongs to a sect that doesn't allow divorce, and whose family is so gung-ho about the church that his having anything to do with a divorce family would mean resigning from his job and alienating his entire extended family.

But then, the writers would STILL have to deal with the central problem in the story, that the hero is an idiot who makes all the wrong choices, because he's afraid to do anything but conform.

The strictures of today’s Woke culture and the constant menace of cancellation would make for a good backdrop to a doomed romance.

A happy heterosexual couple are torn apart by the pressure for him to sleep with black men, and for her to fully transition including breast removal and the installation of generous male genitalia.