There is nowhere else for the heat to go.
Aren't you forgetting that the efficiency of a thermodynamic process is proportional the ratio of the differences in temperature and the ambient. If the Bitcoin mining chip is not as hot as the coils, then it will not be as efficient as the coils were. Also for example a hair dyer needs all the heat transfered within a short period of time, and if the heat transfer is slow not all of the heat may be extracted to the hair and instead wasted to the ambient. So somewhat less than free mining.
No. Work out the actual transfer equations if you like, but it ends up being an equivalence. Energy in = heat out. Or the device self destructs. Certainly true for a room heater. True in practice for a hair dryer, water heater, etc. I'm not so sure about a toaster. That may be a bad application for it.