I've often found that the Tetragrammaton (Shem Havayah) is often vowelized in siddurim and sefarim. Since we b'davkah don't say the Shem Havayah how it is spelled, why are the vowels included?
Also, are the vowels usually included an accurate reflection of how it was pronounced?
I've noticed that in Artscroll siddurim, they do spell out the yud, then heh, then vav, then heh, albeit without the nikkudos. This seems to make sense to me, as then someone reading it would have to go out of their way to pronounce it.
I do understand the difference in vowelization on whether it's Hashem/Elokim verses just Hashem/Ado-noi, but why do we print them in places other than a chumash or a tanach?