The idea that you have to choose between (high) inflation and distributing Steem to many hands (say a billion, to use your number) is false.

There are many ways to distribute coins. For example, a front end or community can require that advertisements be paid for in Steem and can then distribute those coins to its users as rewards. This has numerous benefits as an economic model, including the fact that it closes the loop in terms of value add and value paid out. Any front end or community which allows its users to 'milk' by earning rewards without bringing in eyeballs and ad revenue will run out of coins and go out of business. On the other hand, a community or front end that is successful with this model will bring in large numbers of eyeballs, high ad revenue, and have many users.

This is unlike Steem, where people, including the very largest stakeholders can milk for years while we are bringing in few (net of attrition) users or eyeballs, and there is no natural limit to it. That's the real rich getting richer problem (at least if you want to measure 'rich' in terms of stake rather than actual value).

Proof of Brain maybe could possibly work, in some theoretical sense, but it hasn't been demonstrated to work so far. Yet Steem is still, for years, spending an enormous part of its inflation budget on something that doesn't work. This is contrary to every notion of good business strategy. If a startup has a growth plan that involves spending $X on such-and-such promotions, marketing, etc. and after a reasonable time (months to years, in this case, depending on how you measure) it turns out that spend isn't producing anywhere near the planned or needed growth, then any sensible management will pull back on the spend, iterate on the strategy, and try something else. To just continue to pour money down the drain at the predetermined rate on a failed plan is suicidal.

I think it would be perfectly okay to drastically cut spend on PoB and then, if a successful model could be demonstrated using SMTs, with some growing communities, or if some other credible proposal were made to further modify it to make it really work (say EIP 2.0), then it could be dialed back up. It makes perfect sense to spend money on something that has been shown to work, and indeed is stupid not to.

I like EIP, I was a big supporter and advocate for it. And it has improved things a bit, but not really all that much. There is still a tremendous amount of milking going on every single day generally by large or very large stakeholders (as they have the stake to direct rewards to themselves or within a small group; users with little stake do not), and the very largest stakeholders are still selling their votes to the vote sellers and bots with the highest ROI (and in the process getting richer). There is still a only a very small amount of downvoting, as apathy and fear of retaliation are enough to discourage most from using even EIP's free downvotes, in practice. And most importantly of all, it still isn't working as a growth engine, and there is no data that I've seen suggesting it is on a trajectory to do so, ever.

Unfortunately, the inflation you claim is distributing stake is actually doing more to destroy the value of it as well as in some non-trivial ways, actively concentrating it.