1/ People seem increasingly concerned about the term "daily active users" (DAU).

It's used by other web2 social networks (in SEC filings!) and now other decentralized social networks; we use Meta's definition (below).

Is there likely a better definition? Yes! 

Have we come up with a better methodology? Not yet.

2/ Farcaster social graph is permissionless, anyone is able to come up with an alternative, better metric. You might even convince everyone else on Farcaster to use it!

However, the casual observer on Twitter that sees a DAU comparison between various networks won't care about the nuance.

Moved to /anser

I think DAU is a good quantitative metric to measure growth, and with client filtering you can remove bots.
With /f4r we are working on engagement qualitative metrics for brands and UGC creators, but they serve a different goal.
I have various ideas I started to put down here but it deserves a paragraph article!