I can't believe how much we agree. On almost everything. I've been watching your videos for more than a year now and every freaking time it's like listening to myself thinking. Chills.
I've already envisaged creating a currency (when SMTs come out) where the reward pool for a week will only be constituted of all the burned stake in the previous week. Maybe with an added 1% inflation. Then it's just a matter of getting good sinks, which will also cause a high faucet, and with all of that inflation is kept at a maximum of 1%.
As you said the faucet is great for distribution, attracting users, and will consistently be redistributed to the people and businesses creating the most value for others (if the Proof Of Brain works fine).