There was a (very) fleeting attempt made by some Indian leaders to achieve what you are describing in 1947. But not because of the reasons you mentioned. Before we get there some context is necessary.

The initial demand put forward by Muslim League (henceforth ML) was significantly larger than how Pakistan and Bangladesh look like on maps today. Muslims were ~25% of undivided India's population. ML demanded two 'zones' of India, one in the east and another in the west where Muslims were in a majority. This is what they demanded -

In the east - Entire undivided Bengal + Assam + Native ruled enclaves. Going by present day administrative boundaries, this will be Bangladesh + Indian provinces of West Bengal (sans Purulia and North Dinajpur districts) + Assam + Meghalaya + Manipur + Tripura + Nagaland + Mizoram. In other words almost the entire Indian North East, West Bengal and Bangladesh were demanded as part of the eastern zone. Some additional demands were also made - such as the easternmost districts of present day Indian province of Jharkhand - by some ML leaders but these demands weren't part of the official list.

In the west - Entire undivided Punjab + Sindh + NWFP + A few autonomous tribal enclaves (like FATA) + Native ruled Kashmir + Other native ruled enclaves. Going by present day administrative boundaries, this will be Pakistan + Indian Kashmir (sans Aksai Chin) + Indian Punjab + Himachal Pradesh + Hariyana. The border of the western zone would have been next to the Indian capital of Delhi.

The population ratio in the western zone was 60:40 between Muslims and non-Muslims. In the east it was 55:45. It was an extremely exaggerated demand where outright Hindu majority districts were claimed. Needless to say Hindus weren't going to accept it. So the question is - why did ML make such an outsize demand?

It is argued - and there is disagreement among historians on this point - that ML didn't actually want complete separation. What they really wanted was a loose federation where the Muslims majority zones would be granted very significant autonomy. In 1946, the parties involved came very close to reaching such a deal. Known as 'Cabinet mission plan', a scheme was devised to create an independent Indian federation which will grant the Muslim majority zones significant autonomy. However the deal eventually broke down. ML lost patience and asked its followers to engage in 'active measures', starting on 16th August, 1946.

It went out of the leadership's control. A massive religious civil war soon engulfed the country. Chaos ensued. The parties eventually agreed on complete separation.

This is where your question comes in. As described above, ML's original demand was significantly larger than what simple demography would have allowed. So when the decision was finally taken to partition the country on the basis of religion, they were told - as demanded by Hindus - that the only areas they could claim were those which had a Muslim majority (> 50%) and were geographically contiguous. But the smallest unit of such 'areas' wouldn't be a province as ML wanted. It would be a district (the next level). And depending on local conditions, it would get even smaller like a district subdivision or an even lower level unit - the local police jurisdiction/municipality/village.

This is what cut Pakistan, as demanded by ML, down to size. By making the demographic unit smaller, all the Hindu majority districts of Bengal and Punjab as well as nearly the entire province of Assam went to India. The remaining areas became what you see on maps as Pakistan and Bangladesh today.

When this finally became clear to ML leaders that they were going get way less areas than their original demand, one senior ML leader from Bengal - H.S. Suhrawardy - tried to achieve what you are describing. Like him, a few Hindu Bengali leaders were also opposed to partitioning Bengal. Together they proposed that Bengal, along with the rest of the eastern zone should become a third, independent country. It failed to garner serious support among Bengali Hindus and was soon discarded.

So to recap - ML initially wanted, arguably, a united Indian federation with significant autonomy for Muslims and equal share of power at the center vis-à-vis Hindus. The geographic limit of that autonomy was supposed to be the two zones as described above. Instead they were ejected from the union altogether and got way less share of areas than they expected. And all the while these negotiations were going on, the countryside was convulsed in a brutal civil war that will continue well into 1948. Some 10-15 million were ethnically cleansed, mostly in Punjab. No reliable figures exist for the number of killed. Estimate vary between 0.5 to 1 million. Further ethnic cleansing would continue to happen in Bengal in the east in the subsequent decades.

To make matters worse, Pakistan didn't even get Kashmir, a large, Muslim majority but native ruled province. And independent India and Pakistan would soon fight their first war over Kashmir, starting October 1947.

Given this background, as you can guess, the merits-demerits of being separated by over a thousand miles weren't the primary concern of ML leaders in those days. They decided to stick together and try to stay afloat.