I think we have to distinguish between pious characters and those who are merely holier-than-thou; and also have some ground rules on what the piety is being measured against to do this topic justice. How would a character that's not following something close to one of the Faiths of the Book be judged as saintly?
It is true that many characters that say “pious” or “holy” on the character sheet actually turn out aligned simply Lawful/Obnoxious — the one I remember from local play being an LG dwarf cleric by the name of Aman Naug who came over as very austere and puritanical, and noted as to be one of the first against the wall when the CG revolution came. Most interestingly, when dusted off post AD&D2, as a priest of Aurochs, lord of berserk strength (the CPHB Strength specialty priest type), he became the rather lighter-hearted Noggin the kung-fu barbarian dwarf in very short order. And he was doing a lot of righteous smiting as befitted his faith. Was he saintly?
In a more familiar style, I remember affectionately the write-ups from long, long ago of the Tale of Two Clerics, two pious characters and their unfortunate companion, the rather more self-interested Frank (and all his relatives — replacements — of the same name). They sounded saintly, and certainly seemed to work.
Had I actually completed character generation for Saxum, my character there would have been inspired by Roger Bacon, as portrayed in Blish's Doctor Mirabilis, and would have had a definite background from the Church, even if a mildly heterodox one, from time spent in the University at Paris, a pious inquirer into the majesty of Creation. As it turned out, I don't think he would have fitted the rest of the group, so that's saintly character that wouldn't have worked, but in that case only due to the particular context in which he would have been set.