Beginning to dislike our flowering cherry tree

It was there when we bought the house nearly 40 years ago, in the front garden and quite close to the house. It's very pretty for 2 weeks max, and then there's a mountain of pink 'snow' to sweep up, and nothing else.
I'd love to get rid of it and plant an apple tree instead - I do think apple blossom is the prettiest of all - and at least we'd have something useful at the next of it. Wouldn't say no to a proper cherry tree, either. But I'm beginning to wonder why anyone would ever plant a 'fruit' tree that bears no fruit.