What useful information could solid color and random text leak even if depixelized? I assume the average solid color is just so the new pixelized region doesn't stand out against the rest of the non-pixelized ones, being an average color.

Applying it to an HN comment the result would be a solid average of #F6F6EF (beige background) and #290027 (text), so a solid darker beige with some random black text over, all pixelized. How can any of this be used to recover the original text?

It could speed up bruteforce attacks. Imagine a targeted attack having both an "average color" of the rendered password, produced by known background and foreground colors and a known typeface and also having a strong cryptographic hash of the password, where the hash takes for example ~0.1s to calculate.

The attacker then before trying to hash a candidate password they can first calculate the average color of it to check if it even remotely matches, which can be much faster than the hash function.

Average color could be a rough predictor of password length too, depending on circumstances.

Ok, maybe I had a different interpretation of the scenario OP presented. I read the "solid block of average color" as simply an average of 2 colors, not a weighted average. So black text on white background would always result in rgb(128,128,128) (#808080) regardless of how many pixels of each color you had in the block. The only things that leaks are the color of the background and of the text but these are already known from the surrounding parts.

This makes sense for purely aesthetic reasons because the pixelized block will not stand out against the combination of background + text around it. A white page with black text would have a gray fuzzy area where it's pixelized.

If a weighted average is used and you can determine the fill factor of the text inside the box that would be some information leakage, as small as it may be.

In principle it leaks information, so is always worse practice than not leaking. For example, one could imagine an edge-case where given a set of average-colour password images collected over time, for a password field that has a dynamic in its presentation that is exposed in the averaging, useful information could be discerned and used to supplement other attack vectors.

Say for example, the password field had one of those password strength colour indicators that subtly changed the background or font colour to indicate password strength, and the images were captured and obfuscated at that point. Information useful to an attacker would now be embedded in the colour average.