Brakes are built in:  higher the price, more mining as measured in electricity used.  Miners have to sell Bitcoins to pay the bills.  So, higher the BTC price, more selling there is.

At 10,000, we are already at the 500 million per month for miners.  So you need that amount (more like 50% of it) of fresh money per month to enter exchanges just to keep the BTC price stable.

At BTC one million, we are talking about 50 billion dollars each month.