Thithi is based on moon, and nakshatra is based on star. As moon is more nearby and calculation can be better , thithi is taken for, whereby the relative calculation and time adjustment will be more accurate. Moreover , to take a practical realistic view, all our main ritual festivals fall on Pournami.because in olden days there was no electricity.The only main festival falling on Amaavasi is Deepavali, when we bring light by lighting a number of Lamps.
Then, in calculation Deva varsha ,pitru varsha etc, (the time factor- days and year of manushya,Deav ,pitru etc) it is based on thithi or lunar day and not Nakshatra.
Another deduction can be, that pitru loka is thought to exist on the other side(generally invisible) of moon.Hence thithi, based on lunar rotation is based for pitru sraddhas.
Hence hithi is followed. (IMHO)
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