If I instead of taking the envelope, (equivalently) toss a coin. And let us say I choose 'Heads'. Question: This situation above is it not akin to then changing my mind to 'Tails' -- and so on?

What is the fundamental reason that one should keep flipping from 'Heads' to 'Tails' and back-n-forth, and assume there is more money being made from (equivalent) future iterations.

This is a Ponzi scheme. :-)