That's literally backwards to how this works though. Just because you fire up a bunch of miners doesn't make Bitcoin's value jump - it's the opposite, Bitcoin's value jumping makes it cost-effective to run additional miners.
Miners engaged in mining before I arrived would have the same costs they had before, but now with fewer BTC to cover them, this would force them to sell at a higher price or operate at a loss until they drown the competition.
There are two ways to look at it.
Nope.
Miners have costs to cover, mining unprofitably and holding makes no sense whatsoever (you're literally better off turning off your rig, buying on the market and holding at that point)
You're better off buying them from others at that point.
My dreams of being a millionaire are forcing me to sell this orange for a million dollars. Ergo, oranges will now retail for a million dollars.
Bitcoin production is perfectly inelastic, and Bitcoin itself has no consumption value. You need a different analogy.
If there were only 12 oranges produced on all the trees in the world every hour & it cost $500 an hour to operate your orange farm. You therefore have to sell your oranges for at least $42 to cover costs and make a small income
However now there are only 6 oranges produced every hour (not 12), what can you do to maintain profitability?