Who asked Muslims and Sikh/Hindus to slaughter/rape each other in '47 in Punjab ? Don't you think antagonisms were thus already there ?
If you're a liberal, there's a liberal scholar in Pak, Yasser Latif Hamdani, who said that the biggest win of Partition was the rise of a Muslim urbane middle class, which pre Partition only existed in some pockets of the Mughal élite (thus the Urdu speakers dominating bureaucracy and other professional fields at Partition) ; if there wasn't Partition, the urbane middle class in places like Lahore, Rawalpindi, etc would have been the Hindu banya, the Punjabi-Khatri's, while the rest would have been living like Dalits or Muslims in India for that matter, and you talk of the cricket team, but who tells you that the perennial 6-7 Brahmins in the playing XI would have let all the Imran Khan, Wasim Akram, etc to even get there ?
In fact what you should get first out of your head is the very idea of some hollow "united India", it never existed through popular sentiments, but only through forced external domination, often foreign to the peoples of the land (Maurya, Mughals, British, etc).