For all practical purposes INR is transferable with Taka, at least in areas bordering BD. I live in Kolkata and hear a lot about this stuff, unlike Indo-Pak border Indo-BD border is very active economically. This activity can be turned into a national asset for both nations if channelised correctly.
I do not see a possibility of a future common currency due to multiple technical issues, but even if BD were to join UPI payments system, the currency issue would be rendered moot. It will benefit everyone (except the banks which charge fees for currency conversion).
Indian customers need to use a foreign currency, or their credit or forex cards to pay at international merchant outlets but with the 'UPI international' payments feature, PhonePe can now use their Indian Bank accounts to pay using UPI.
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Nepal and Bhutan already accept INR for payments in many places, especially tourist attractions. I had used Gandhi to pay in Pokhara, Kathmandu and Paro. If we make a common currency along with SL and BD, it'll be beneficial to all. SL has woken up from it's CHina-dream and is now looking to build economic relations with neighboring countries.
BD is crucial to India as it's the gateway for NE India. NE is our least industrialized region and needs massive industrial reforms. Common currency would be good for all.
But, I think keeping Pak and Afganistan away for the moment might be a wise choice. Pakistan currency is too volatile and Afganistan has an unrecognized government.