Let's do some math;
Rewards a few hours ago were around 1.7 Mrai per recaptcha.
It costs about $1.2 for services to solve 1000 recaptchas for you.
So for 0.0028 BTC ($1.2) you get 1700 Mrai which means you're breaking even at 165 sats per Mrai.
And it's safe to say that at such low rewards as 1.7 (which translate into over 200 recaptchas being solved every minute) only captcha solving services and maybe some super enthusiasts are solving recaptchas.
With all that said I think the price will decrease probably below 200 in a few weeks.
I really love your analysis. However, I would like to present a different point of view.
This is a question of demand and supply. You are saying that the price should drop, but I would argue that it would only do so if there was no demand. If there is demand then instead of price falling down, the rewards will fall down until they find an equilibrium.
If you are saying people will gladly get paid $1.2 for solving 1000 recaptchas, then they'll provide more and more supply, until it reaches that price. The comparison to Bitcoin mining is fascinating. The difficulty of the network self-adjusts.
I agree but what I wanted to point out is the method of distribution thriving to be fair actually fails. It aims for fair distribution but it's one of the easiest methods to game and so it's being abused - for lack of a softer word.
In return that turns away new people because they get negligible rewards leading to poor distribution. And while I missed the early days of the distribution it seems early adopters own a significant chunk of the current supply of coin which again, is poor distribution.
The only positive thing I can see is that similar to PoW there is a cost of producing a coin which should create a floor price.
But of course there's the possibility of the opposite, meaning the low supply driving the price up, but I'm skeptical of that.
It would be nice if we had some transparency regarding the payouts. For example knowing the average reward per reptcha for the previous 24 hours or so.
Or if we had a proper, browsable block explorer, of course. Without that the coin lacks transparency which makes it hard to justify investing in it.
I totally agree 
