Re: Starlink Visors
I found this paper, might be of interest to you: "Review of black surfaces for space-borne infrared systems"
https://wp.optics.arizona.edu/optomech/wp-content/uploads/sites/53/2016/10/persky-1999.pdf
The paper mentions several uses for painting certain parts of satellites black, the most common being to protect optical sensors on space telescopes from stray light reflected into it, or as a calibration surface for telescope instruments to measure from. It does say the article is intended to be a broad overview of black surfaces in space, but specifically painting a whole sat black to reduce the light reflected back to earth was not mentioned.
So it does talk a lot about out-gassing of the paint/coating, and durability of the micro-structures on the coating's surface in space, if the black relies on surface texture to reduce reflectivity. Doesn't talk about how much heat gets absorbed.
However, one bit I found VERY interesting is the sections about temperature do mention great "emissive" performance. At one point they imply a black coating on anti-sun-facing side can help cooling, to the point where a failure-prone liquid radiator system could be designed out of a satellite. See page 2, paragraphs 2 & 3.
Also see page 7.
This tells me that it could be entirely possible for Starlink sats. I believe only the bottom (earth-facing) side of the sats reflect light that we see post-dusk/pre-dawn, so even if a black coating produces quicker heating, the time windows where heating is occurring should be minimal, and then once the black side of the sat is in earth's shadow (or on the sun-side but facing anti-sun), it should provide extra cooling.
All in all, with a slightly different thermal design, I think they could definitely do it if they wanted to. Source: whale biologist.