You don't hear a lot about Pope John Paul.
You do hear quite a bit about his successor, Pope John Paul II, and rightfully so; but JP I, not so much. Other than having possibly the shortest Pontificate in Church history and dying under mysterious circumstances, there is no serious discussion.
That may all be about to change.
Pope John Paul I, born Albino Luciani, has moved closer to being beatified after the Diocese of Altamura-Gravina-Acquaviva delle Fonti in Puglia, southeastern Italy, concluded that a banker, Giuseppe Denora, was cured of stomach cancer in 1992 after praying for the late Pope’s intercession.While it is much too early to start calling it a miracle, the case has been forwarded to the Congregation for the Causes of Saints for further investigation. Usually, getting past the ordinary (the local Bishop) is the hard part; many Bishops are reluctant to have the kind of "disruption" in their Diocese that comes from investigating miracles and causes for sainthood.
Among other things, it takes two attested miracles to be declared a saint, but it only takes one to be beatified. Even if the cause never progressed beyond that stage, it would still mean that Albino Luciani was in Heaven. (Not bad!)
I'll defer to any Canon lawyers, but I think even Servants of God get to go to the Big House.