Am I missing something. Is the block reward glued to the square root of the difficulty indefinately? That would create a situation where at difficulty 1M the block reward will be 1000, this is hyperinflationary to anyone who mined @ br 100, will likely cause everybody to sell mined coins immediately and very few people to want the devaluing coins. Please correct me.
Currently, yes the block reward would be glued to the square root forever. While at difficulty 1,000,000 the reward would be 1,000, each coin would be much harder to mine (10x harder, as 1000 would be produced for each 1M block, and each 1M block is 100x harder to mine than a 10K block) and so the coins would enjoy a gain in value over time, without the hard explosion (and subsequent crashes) that other Cryptocurrencies have had to deal with.
Essentially, it is playing supply and demand economics with a twist. The more demand, the more supply, but supply doesn't scale in a linear fashion.
The non-linear scaling makes faster hardware not cause hyperinflation (as a 1:1 reward would, as more coins per $ would be made in the future), however the scaling does mean that early adopters won't be the only people to make a profit, and large market swings will be reduced.
It would take a 100x increase in the total mining hardware on the network to boost up the block reward by x10, and therefore the coins do become more valuable over time. However, people aren't as likely to dump them quickly (mined 1000 roots in 6 months, now that 6 months of time with the same hardware would only get 100 coins, let's say) as it would not be as sharp of an inflation that a fixed-difficulty coin (such as has been seen with Bitcoin) experiences.
Hopefully that clears it up? It's a bit hard to explain.
Everything you said about requiring more hardware with respect to difficulty increase can be said of any coin. But almost all other coins have a constant block reward. Root block rewards increase proportional to difficulty. Hence, it is hyperinflationary. Moreover, there is too much 'hand-waving' in your argument. You assume demand will be there when and if difficulty reaches 1 million, but it's quite possible for miners to mine and raise difficulty strictly out of profitability
relative to all other coins. If I drew the graph of Root's price versus time, it will tend to zero rather quickly, whether you like it or not...
Yes, the difference with the increased hardware is that that increase in hardware is now pinned to the block reward as well.
Inflation of a currency is when a currency's buying power is reduced. With fixed-reward currencies, the buying power increases at ridiculous rates as difficulty increases. For example, one Bitcoin back in January was worth around $20-$30, and had that much buying power. Since the supply of Bitcoin doesn't increase with increasing demand, we end up with one Bitcoin at one point being worth over $250, a 10x jump in a matter of months! With 'root', however, the block reward would increase with increased demand, so while the value would still go up and down, it would correct faster (buffer), as with less profitability, less people mine, so less coins are produced an hour, and vice-versa.
It's true we don't know what it will really do once it hits the market, but seeing the economic patterns Bitcoin has taken, it makes sense for root to work.
The main force that would cause its price to drop to ridiculous lows would be a general lack of interest in the coin. The coin's economic ideas itself would not run it into the ground, as it adjusts to supply/demand.
It wouldn't be hyperinflationary, but instead would be anti-deflationary. Compared to Bitcoin, it would be inflating, but when pinned to fiat it would simply resist movement in both directions. Our view of currency has been slightly skewed by Bitcoin. A currency usually does not deviate as much as Bitcoin has, and when a coin makes less profit for initial investors it could be considered inflationary relative to Bitcoin, but the currency would not lose buying power, but instead would not gain as much, increasing its stability.