In looking to BPHS Chapter 48 to resolve the issue of whether daśā are to be based on the Moon or something else, we find NO CONCLUSION from the text. The key text where the issue would have been solved is is 48.13. He says

वहिभाज्जन्मभं यावत्
vahi bhāj janma-bhaṁ yāvad
“from the birth star….”

This is all that is said.
No definition of “birth star” is given.

The three most acceptable meanings of “birth star,” in my opinion, are:

1) The nakshatra of the day on which one was born.
2) The nakshatra occupied by the moon when one was born.
3) The nakshatra rising when one was born.

Option 1 will prove that it cannot be used, when we read the next text, which teaches us how to deduce the portion of the first dasha. That text will give us a formula [(eD / tD) x dL = d1L], where eD relies on the “birth star” being resolved to a degree. Daily nakshatra cannot be thus resolved.

So we are left with Options 2 and 3, of which Option 2 is obviously the much more popular choice. Due to my studies over the years, however, I lack the popular confidence that it is the one and only definition. I have found much reason to consider “birth star” the rising nakshatra.

I personally believe the lack of clarity is intentional, and that the dashas could be calculated from either Option 2 or 3. I am not sure what the criteria would be to determine which option is which appropriate for which native, but it does not take much effort these days to calculate both and compare them case-by-case, to decide per case. Another option is that both may work simultaneously, in concert, in some relationship 1:1 or where one is subordinate to another.

In my personal experience so far, the ascendant based viṁśottarī has more initial accuracy.