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
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$$
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).