Not all requests are the same and they need to be treated differently. Some requests are rather optional and it's probably better to timeout if they don't respond in a timely manner so not to use up more resources than needed. Other requests, like payments, for instance, you probably want to give the best chance for it to succeed. So, no timeout is likely a good idea. If the actual TCP connection times out or is closed by the server, we can hope it was good enough to realise something didn't go well and rollback. So, we are probably safer to assume it didn't go through in that case.

When it comes down to UI there are even more options. Since you have a human on the other side, you can transfer to them the responsability of deciding when to timeout. The UI certainly shouldn't become completely unresponsive while a request is being made.