bitcoins are backed by the proof of work and elecricity used to mint the coin
I think Bitcoin is already backed by hardware power and miner's know-how.
Bitcoin is backed by MATH.
This is a myth I wish would have been rooted already.
"X is backed by Y" means there is a guarantee that you can hand over X and receive a specified amount of Y. In the "electricity / hardware power" this is reversed - a mining rig can transform electricity to bitcoins, not the other way around. If someone finds a machine that can convert bitcoins to electricity, let me know. Also, the conversion ratio isn't fixed.
"Math / proof of work" only guarantee that a bitcoin is a bitcoin, it doesn't guarantee that it has any sort of value. To be of value, Bitcoin needs both
the math to protect it from loss, theft, inflation, counterfeit and double-spending, and
the people offering goods, services and other currencies for it and believing in its long-term prospects. If you take just the first without the second you get something worthless (see also testnet bitcoins).
Now for the OP... Even if you could somehow make it scale, attempts to put a floor on the exchange rate can backfire due to anchoring
effects. Suppose "The Bitcoin Floor Company" enters into a legally binding agreement to always offer $0.01 per bitcoin. This only requires a $210K reserve and presumably is a net positive - people will be guaranteed that no matter what happens, a bitcoin will always be worth at least $0.01. But when people will try to form an opinion on what a bitcoin really is worth, they'll think (whether consciously or subconsciously) "Well, this company backs bitcoins by $0.01, so I guess they're worth just a little bit above that". This can cause a decrease in its valuation.