Tolkien had not decided on the significance of the ring that Bilbo found when he wrote the Hobbit. Indeed in the first edition of the book Gollum wagers the ring as his stagestake in the game against Bilbo.
So the out-of-universe reason for why the ring of power grants invisibility is that when it was found it solved the need for the protagonist to get the power to turn invisible. This happened at an out-of-universe time when there was no need for the ring to be the master ring.