you'd have to ask a Tibetan buddhist about the purpose of their mantra. Rebirth mantras exist in Chinese and Japanese buddhism too in Tendai & other sects.
As a Jodo buddhist we call on Amitabha's name as it says to do so in the Pure Land Sutras. Using Sanskrit Namo Amitabhaya is perfectly fine, in fact Chinese temples have tried introducing this to Westerners instead of Omitofo, when I attended a Fo Guang temple the old high ranking Chinese monk led us in this chanting & told us the Brasilian members prefer it. He thought it was great.
I chant Amida, as my teacher was from the Japanese tradition and it's 15 years later:) otherwise I'd be chanting in Sanskrit, it's so beautiful & I understand so much.
Do check out Imee Ooi's Pure Land Dharani on youtube, it's in Sanskrit & so beautiful.