Hawking radiation has never been detected because the temperature of a typical black hole is miniscule. Using the formula, the Hawking temperature of a solar mass black hole is about 0.00000006 Kelvin.pic.twitter.com/l7QseBt1oa
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It's not that you "lose" it. It's just that it's in different units. And is makes sense that free space should have a permeability of unity, as opposed to some clunky number with 5 different base units.
If you know what is epsilon(0) physically then you set it to one. But it is my humble opinion that we don't know well enough this constant. Thanks for mentioning the swapping of space and time inside BH, I heard of it I am not a specialist. Analogue gravity might help...
It doesn't have to do with setting it to one because of precision. The way units work is that everything is ratios of some "base" unit. There it's just a matter of what you choose as the base unit.
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