I can think of many (admittedly anecdotal but I think valid enough) examples. Just off the top of my head, Facebook is full of people who plainly use their real name and operate their account within the context of their real, in-person or professional circles of friends. Despite this, many of these people regularly place comments or posts that are blatantly rude, racist, spammy, fraudulent and so forth. It's a very common phenomenon and with little repercussions in most contexts. Social media and many other digital media forums are also loaded with people who regularly defraud others in ambiguous ways with little to no legal consequences. Imagine, if you go to a typical city police station in, say, nearly any North American city and report a non-violent property crime, the police will often straight up tell you that aside from filing a report, they'll do next to nothing else. Now imagine how much less they usually care in the case of legally grey cases of digital fraud below a certain genuinely large or frequently repeated amount. Even if you have a person's completely real name to point to, many criminal investigators just won't care, it won't be worth their time unless it's part of a massive pattern, involves lots of money, or affected someone with major political or social clout. A lack of anonymity means nothing in these contexts. At the same time, a lack of anonymity does indeed expose many other people to all kinds of unfair abuse that they have little recourse against.
As for your second point: The topic of dis/misinformation is a whole separate can of worms that I won't go into in detail right now, aside from saying that it's loaded with assumptions and shifty, politically charged definitions of what really is disinformation. This aside from the fact that I sincerely believe people have a right to share even stupidly mistaken opinions of X or Y, regardless of what certain self-proclaimed intellectual betters think should be allowed. With regard to your other points about crime and harassment, I refer you to my point above: firmly verified IDs barely dent these things. However they definitively do open people up to surveillance, censorship and the illegal leaking of vast troves of sensitive personal data from hacks of "secure" ID verification systems run by governments and corporations. To me, the trade-off is clearly in favor of giving people a basic right to hiding their real identity in all but absolutely necessary situations..