I have heard about gambling sites seized people's money when they are gambling from restricted countries but have you experienced this on any exchanges?
Never faced a situation like yours and hopefully it never happens.
I have done KYC on local exchanges and only once and have not experienced any problems although I sometimes forget to turn off my VPN to access the exchange account.
I am very careful if the KYC that is done to have to upload documents, if you can avoid this by changing exchanges I think that would be much better.