I think these two tenses are not interchangeable at all in any context.
He plays the saxophone every night.
This is something that he does habitually every night. Every night, he takes his saxophone and plays it.
He has played the saxophone every night.
With this sentence, I'm thinking that he started playing the saxophone at some point in the past (let's say when he was a kid) and has been doing that ever since every night up to the present. We can even add that additional time information into the sentence.
He has played the saxophone every night since his childhood.
In most cases, with sentences like this one, it would be only natural to almost always add some additional time information into the sentence to qualify since what time the action we're speaking about has been happening.