If the miners multiply in numbers, their individual "influence" is proportionally diminished so that the overall "influence" of the miners remains constant to what has been hard-coded into the protocol: a steady source of liquidity that is as hard to produce as bitcoins are valuable. The value of bitcoins is externally imposed by the market and the miner crowd reacts. The market is the dog, and the miners are the tail being wagged.
The emergence of miners is an entirely mechanic phenomenon, is there is value in mining someone will do it. Rational miners can't "press the 'stop' button and wipe out the whole thing". An individual miner can behave irrationally but his place will soon be taken by a rational miner. Hoarding at the miner level is inconsequential - the miner buys BTC with his resources. To affect the price he has to buy at a loss, to mine for hoarding when it's cheaper to buy on the market, in other words to behave irrationally.
To say miners can chose to stop Bitcoin is equivalent to saying that the drug cartel can end cocaine abuse. Sure, if all individual traffickers stop producing and selling cocaine, they could theoretically stop users from obtaining it. However as long as there's a demand someone will fill it, the drug cartel is a rational supplier for the existing drug demand.
Miners trade. There is no point to mine if you don't trade them, whether for cash or for goods/services. The more miners there are, the more traders there are. While it is not true that all traders are miners, it is much safer to think that all miners are traders.
The more traders there are, the more liquidity there is.
Liquidity influences the economy (lot's of buying and selling aids merchants) and thus price.
There are so many angles from which this can be approached, and this doesn't even include arguments for unknown effects of miners.
If people know exactly what influences what, then how come nobody knows (not predicts) where the market is going?
I agree with you original proposition that the miners influence the price. That influence, compared to the influence from other forces, is quite negligible.
Your next proposition that the miners trade is much more interesting, although false - when the miners trade, they do not act as miners but as speculators.
See my other thread where I discuss the two contradicting groups in the Bitcoin market https://bitcointalksearch.org/topic/contradicting-requirements-how-to-extract-most-out-of-btc-46116
I also do not agree with your proposition that liquid market aids merchants - I would say, exactly the opposite - the merchants prefer stagnated currencies.