The thing about this, loosely speaking, is that there's bias and variance. The issue with tests is that there's huge variance in them. Out of your life, how much time is spent actually taking it? With the GRE or SAT you're talking a few hours at most; the same thing could be said of most standardized tests.
The problem with this is that now you don't just have bias, you have this huge error/noise/variance associated with the test score. Maybe you don't take tests as well as the person sitting next to you. Maybe there was something weird the day and time you took the test, but it wasn't enough to declare the test invalid because of financial incentives. Maybe it makes assumptions, like that everyone taking the test comes from a common educational background, that are irrelevant to the actual thing the test is measuring. Etc etc. So yes, it predicts things, but if you look at studies, it does so relatively weakly in the grand scheme of things, and even more weakly with reference to even longer-term variables past first-year GPA.
The issue is that yes, the SAT, GRE etc is providing some information. I agree that ideally it shouldn't be thrown away. But today you have this opposite extreme in many cases where it's taken very much at face value, as an error-free quantity, or only minimally so. It's difficult to do anything with. Let's say you have someone apply. They're Asian, or white, or black, or whatever. Their test score is relatively low, but they have incredible background, GPA, etc. How do you interpret that individual test score in that context? The appropriate thing to do is to treat it as one bit of information, so that if everything were uncompetitive, it would support that, and if everything were competitive, it would support that, but in the scenario described it's kind of off. If you ignore it though, do you really need the test? If you blindly let the test overrule other things, is that appropriate?
Tests I think have become a kind of liability, in that they are useful, but their use is superceded by their misuse. There's always this one person or group who argues that the test score should supercede other bits of information because it's "more objective" ignoring all of its noise. It's almost like information that becomes dangerous because how it's leveraged by admissions committees, politicians, etc. in a way that far exceeds its validity. It's like having a tool that people can't use correctly on average -- if some product were on the market that led to lots of problems because people were misusing it, you might say the tool isn't the problem, people are, but if people were misusing it that much, you might still take it off the market because that's still critical.
I feel like there's a lot of this -- it's not just tests -- where a lot about a person gets reduced to a single number, or a couple of numbers, that are treated as fixed properties of that person, which is not true. A number may be more objective, but if its meaning is hazy enough, the objectivity doesn't matter.
This all may be moot, because I suspect a lot of this is just due to coronavirus-specific issues and tests will get readopted later. But I could be wrong.