Making links recognizable in ways besides color is a basic accessibility requirement; in body text, underlining them makes their starting and ending locations obvious. I've recently decided to make a very personal exception:
Wikipedia articles are full of interesting links. While this is great for letting me discover new topics, the links tend to let my ADHD take the wheel. Speaking strictly for myself: removing link underlines on Wikipedia articles actually improves accessibility. De-emphasizing links helps me stay focused on the current article.
I think this speaks to the need for customizability by end-users. Users should be able to dictate link appearance, and pages should be robust enough to handle these changes. Of course, this is a bad idea in a world with JavaScript enabled by default (and with an ever-growing number of poorly-documented client hints) because it will only increase fingerprinting. This is why we can't have nice things.
