Well, maybe if you wrote it like this:

mandatory_leading_letters = "^\w+"

optional_suffix = "([-+.']\w+)*"

domain = "\w+"

domain_suffix = "([-.]\w+)*"

tld = "\.\w+([-.]\w+)*$"

regex = "{mandatory_leading_letters}{optional_suffix}@{domain}{domain_suffix}{tld}"

Then you could understand it? Seems to me the trouble isn't with regex but with the decision to write a regex without trying to make it understandable. It is also possible to minify your onto one line in some languages or otherwise obfuscate it; should we then condemn it?

If the author had to fix a multi-line regex, I hope that in the process, they understood it enough to break it up into pieces so that the next time it would be more possible to debug.

Regex are pretty neat. They are often not the solution. I would not want to use lookaround for example. But also, they are really useful in a lot of cases, and I would hate to not use them because they're capable of being obfuscated.