The Buddhist teaching of no-self (anātman) is better stated: overcoming the false self. If one decides to read Buddhism this way it ceases being so enigmatic.
At the same time, we can see that Buddhism is a path of transcendence which is about overcoming the powerful attraction of the false self (anātman). Nowhere in the Buddhist canon did the Buddha teach there is no self (P., natthattā).
Adding to this, the Buddha also teaches that no-self is suffering (yaṃ dukkhaṃ tadanattā). This is not a good state to be in, in other words. Logically, the Buddha would not teach no-self as a refuge (saranā) from suffering.
But if our actual self mistakenly yoked with a false self, yes, there would be suffering. And we would have to learn how to overcome this suffering by first comprehending just what the false self is.
But the modern Buddhist is not interested in learning anything about the false self. Sometimes I think that modern Buddhists, who are agnostic or atheistic, imagine that Buddhism is a religion just made for them. It is not. Buddhism is perhaps the most profound religion on the face of this planet. When we follow its path it gets more profound.