How does money get out of our thoughts? Focusing on any activity does help but can we live a day of adult life without thinking about money — both cases you described — not enough for what we think we need or enough so that we are afraid of losing it...
Finding the balance and peace of mind seems like a very important skill. Something related to confidence, acceptance, a mindset of abundance...
At least in the current conditions, I do not think that we can excise the thoughts completely.
This is the right direction though - confidence is a big one if we consider having the skills/belief that whatever happens, we'll be okay.