Umm many parts of India, especially the cities, are more modernized than you think. India has a very active dating culture, and usually it is the rural areas that are still bound to the traditions you describe. Most families don't judge based on Caste anymore, especially the educated ones. Sure there is still prevalence, but definitely not in the more educated areas.
Either which way you look at it, it is creepy. Here's why.
Situation A) The girl is traditional. Then she is bound to her tradition. In which case getting a poem would be insulting and would be forcing her to go against her tradition, and would totally be disapproved in the idea of the family. This isn't arranged, the guy is a stranger for all intents and purpose. For that reason, it isn't exactly the proper etiquette to begin with. Arranged marriages are more upfront and not a matter of choice. In this case, he chose girl. Fuck this is even ridiculous to bring up cause it's laughable. What I'm saying is, if the guy and the girl were traditional, this would never be a method of interaction or sharing of affection unless they are already together. So the main point everyone is arguing for still stands.
Situation 2) She isn't the traditional. In which case a lot of the dating and the general etiquette that goes with it is very similar.
There is no situation in which an unsolicited romantic poetry would be acceptable in a traditional culture. And it's a bit out of touch and weird in any other situation.
It was nice of your to try and defend it, but this has nothing to do with a culture built on caste or arranged marriage when a random guy is trying to confess his love to a girl through poetry. This is not an approved, acceptable, or normal way of doing romance in the culture except for in their movies... even then.. it is usually mocked in newer Bollywood movies. I don't know why I'm defending this here..