Why do many anime OPs and EDs have onscreen lyrics?
I think this is only common among shows aimed at children. All of the examples you gave were shows which are, at least partly, aimed at children. Having karaoke for the song helps the younger viewers sing along, and also has some educational benefits in terms of learning more advanced characters. If you watch anime targeted at older viewers, they rarely have karaoke.

It's also notable that those anime aimed at younger children are using only very common kanji that even children would probably know, and is giving furigana. Those aimed at older children tend to have more complex kanji and sometimes omit the furigana as well. This isn't apparent from just the exam