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The only thing that I've seen cited as potential evidence either way is that one neutrino, with an energy too high for other mechanisms that we have thought of.

But it is just a single neutrino. And it may be produced by a mechanism we haven't yet thought of.

The black holes that we know about are large. Large black holes are supposed to emit so little radiation that we'd never be able to detect it.

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If the hawking temperature is higher than the CMB, would there be any net evaporation at all?

A BH needs to be truly tiny for it to be hotter than the CMB

Large black holes do have significant accretion disks that do impact their visibility and can and will spew forth vast amounts of radiation. Anything caught in their event horizon gets pulled in and is never seen again. Anything near it bumps into other things in orbit around it, which lights it up like a candle.

Note that there is also a 'weight class' of black holes that are significantly large that their event horizon would be visible to the naked eye, but which don't have an accretion disk. We currently don't know enough to make scientific estimates on how many of each weight class exists.

That is light coming from the accretion disk, and things falling it. The light does not come from the black hole itself.

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