Actually the cost of mining puts a soft price floor on Bitcoin. When prices touch the cost of mining, they face heavy resistance since miners rage quit at that point
Not really, the supply of bitcoin is, except in the short term (< 2 weeks), independent of the amount of mining effort. And that's all that really matters (especially because there's no single price where all miners stop making a profit, and miners will continue to mine and sell even when they are no longer making a profit just to lessen losses on hardware).
and if miners rage-quit then those who are left will make more bitcoin per unit of energy, thus lowering the cost of mining... rinse and repeat and you can go to 0$$