I wonder how much random noise (or other randomness) would have to be added to the pixelated version to make this method unusable.
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This is what you actually have to do with websites, e.g. when you want some content blurred when it's behind a paywall. If you leave the original text intact, people can just remove the CSS blur in dev tools.
Some implementations get this slightly wrong, and leave the placeholder content visible to accessibility tools, which sometimes produces hilarious and confusing results if you rely on those.