They will face legal problems. SEC Nigeria will take legal action against such exchange and possibly could lead to fine or criminal charges and such exchange could also lose public trust as they would be seen as non-complient to regulatory requirements exchange and as such may loss operating license to operate in that jurisdiction ( license revoked)
The government influence every industry that operates within its terrain, and when they have some sort of operational disagreements, the company leaves the country and find another suitable place for its operations, or stop offering that service to the country, just like Binance and Nigerian naira. I believe there are lots SLA breaches that the government demanded from them and Binance had to uphold their integrity by suspending that service instead of compromising on their standards.
If they disobey the directive of the host government, they would not only loose their operating license, but their reputation is at stake. furthermore, they can even be flagged as a terrorist organization by the host country and they would lose patronage from the Ally's of the troubled country, further dragging their reputation to the mud and losing more customers in the process.
They may take time to complie but will eventually complie at the end. The directive to delist Naira trading from exchange were sent to all the crypto exchanges and they are complying to it one after the other. As long as your server is hosted on a centralized server, you can't escape it.
Yes, Nigerian Government fell out with almost every exchange and the problem here isn't the exchange, its the government seeking ways to coverup for the level of devaluation the currency is facing now, Exchanges give the benchmark for the current value of the every currency from the stock market and that's enough exposure to their bad government. The fact that P2P presents their flop to the advantage of traders weakens them since they can't manipulate it or take heavy taxes from those transactions.
The government are used to fighting whatever they don't exert total control over, but the Nigerian government is going way too far in their fights against crypto.