mining doesn't influences the highest price. but influences the lowest, because under an x price the mining costs more than the mined coins.
Please explain how it puts a lower limit on the price. If the cost of mining is higher than the value of the mined coins, what exactly causes the price to rise? How does the cost of mining prevent people from selling for a lower price or encourage people to pay more?
Nobody said that the price will rise. Probably if the coin lost all of it interest, goes right to our cryptocemetery.