The sum of fresh BTC dumped on the market by all miners combined is always about the same: there are 300BTC generated per hour regardless of the number of miners. If miners are evenly split between dumping 50% and hoarding 50%, there will be 150BTC dumped on the market per hour whether there is 1 miner or a million. All that changes is the amount of return you'll earn on a given power investment.
Yes, they "influence" the price, but it's a fixed influence that the miners themselves don't control in scale, other than choosing to sell or not (the same as anyone holding BTC does).
So we agree.
It's whether they do or don't, not how much.
Generally, yes, the bell curve will win. Though it's not necessarily safe to assume the bell curve at all times.
You would predict 150 BTC especially during times of low volatility. However, suppose Bitcoin really catches on and the deflationary trend sets in.
As more and more miners watch the price steadily rise from 30, to 50, to 100, to 500, and beyond, the incentive to hoard increases, or the % of mined coins sold may decrease. The opposite is likely true for inflationary periods, if only slightly. Psychology is the factor that math isn't accounting for when determining the influence of miners on price.
Though in reality, I'd say it's an equal influence. In other words, I think miners and value are entwined.
Every BTC coin is a mined coin. The only times those coins have changed hands is, well, through exchange. Not computer automated exchanges, but people exchanges (or at least people that taught bots to trade for them, thereby transferring their own intentions into the transaction). Every mined coin came from a miner, and thus every coin (which gains value in an exchange), and the value of every coin, is influenced by the number of miners.
Even more simply, there would be no BTC were it not for miners. Miners gave rise to Bitcoin's potential for value. Without miners, there could be no BTC value. And, if all miners quit now, there would be no confirmation of transactions, and thus Bitcoins would be valueless (nothing confirms their value anymore).
What I am getting at is that Bitcoin is a computer program, and Bitcoins are generated and confirmed by computers. But only the miner hits the 'go' button and sets the whole thing in motion. And only the miners, or potentially those who stop the miners, can press the 'stop' button and wipe out the whole thing.
Miners are an absolute necessity for Bitcoin's value as the current program stands.