... how do other countries allow them.
Because their IT department does its job & ours don't. Let me try to explain:
Say you have 1 crore white and another 1 crore black money. You use this to build a house worth 2 crores & wish to use this black money. You declare the government that the value of this house is only 1 crore and declare this amount on your tax declaration, but you pay the builder 1 crore through proper payment channels and remaining 1 crore in cash, since it is black money.
Now, try to imagine you are this builder. How do you spend this money?
You can't! All you can do is spend it in other black channels. You can try to imagine a situation where you try to convert this money to white and you will find yourself in the same situation where we started this example from.
What happens in real life is that the builder declares that he earned 1.5 crores to the IT department and keeps the rest of the cash undeclared. (which is still difficult to do since he only has a legitimate receipt's copy for 1 crore and he has to create receipts. Who does that?! People hide receipts, not create them!!)
Now, our IT department simply taxes the businessman for 1 crore and the builder for his declared amounts.
Yes, our IT might raid the builder in search for undeclared receipts or cash and take necessary actions. But our IT department never balances the books since India is huge and it would require a lot of work. If they do they'd realise that the input is not equal to output.
Thus if you simply balance the net money entering a group of people and the net money leaving them, then black money can never be converted to white!
Most developed countries allow bitcoin ATM because their IT departments does this work of balancing the books year after year and thus they have tight control over their fiat.
