This isn't a full answer to your question, just some points you might want to consider in refining it further.

First, Punjabi actually does have a non-Arabic script, widely prevalent in Indian Punjab. Punjabi has two scripts: Gukmukhi, which is used by Sikhs and Punjabi Hindus, and Shahmukhi, which is used by Punjabi Muslims. Gurmukhi is related to Devnagari, and is an Indian Brahmic script. Shahmukhi is Persian-Arabic.

I think a better historical way of looking at it is that after the creation of Pakistan in 1947, Urdu was declared the official national language. Therefore, all Pakistanis (including Pakistani Punjabis) are taught the Urdu script, which is Persian-Arabic. So Punjabi is also written in the same script in Pakistani Punjab.

Meanwhile in India, Gurmukhi never died out and is far more common than Shahmukhi. India never declared a national language that everyone must learn. Punjabi remains one of the 20 official languages in the Indian constitution. So there was no replacement of Gurmukhi by any other script.

The situation in Bengal was different in a few ways. First, the Bengali script is ancient, going back to Pali, just like Devnagari. 2,000 years rather than the 400-odd years for Gukmukhi. So it was much better established than Gurmukhi, and used far outside Bengal in places like Assam, Manipur as well. There are over 300 million people who use it (5th most common script in the world), as opposed to Gurmukhi with about 20 million. So there was a lot more inertia in Bengali than in Gurmukhi, it was much more resistant to change.

Second, if you look at enforced changes brought about politically, the situation was different. In Pakistan, Urdu was established as standard and was legally enforced in schools all over the country. But in East Pakistan (now Bangladesh), there was a strong resistance to West Pakistani culture. Bengal has an ancient culture and historically high levels of literacy, a rich tradition of literature and poetry. They were unwilling to give that up to the West Pakistani Urdu hegemony.

These frustrations eventually boiled up into the Bangladesh Liberation War, but even through the 40's to 60's there was a cultural "war" between East and West Pakistan over Urdu hegemony and homogenization versus the preservation of Bengali culture.

These things probably played a part in why the Bengali script was never replaced. Plus, of course, the 100 million+ Hindu Bengalis in India who never cared about Urdu and saw no reason to switch to the Persian-Arabic script. They carried a lot of weight and contributed very heavily to Bengali literature. The subcontinent's first Nobel Laureate was the Bengali poet Rabindra Nath Tagore. There was prestige in Bengali.