The following line is included in wanikani’s definition of the meaning of 訪れる:
“What makes it different from 訪ねる, though? With 訪れる, you tend to be doing something for fun but with a purpose.”
However, it it not 訪れる, but 訪ねる that has the nuance of implied purpose. It is the opposite of what is described here.
I’ve found many definitions online, but here is one for 訪ねる: 「尋ねる」「訪ねる」「訊ねる」の意味と違い - 社会人の教科書
“「訪ねる」の意味合いは、「訪問する」というものです。ある目的の元にその場所をおとずれたり、ある人に会うために、その人がいる場所へ行くことを言います。”
That’s interesting, I never really thought about it and took what WK wrote for granted. I searched a little and while the few dictionary entries on the internet just seemingly refer to both words as synonyms (aside from what you posted), I found another source in Japanese for learners which describes the difference between たずねる and おとずれる pretty clearly:
Here’s the まとめ section on that page, which shows some other differences on their usage as well:
「訪ねる」は「人」や「場所」以外に使うことができない。
「訪れる」は「場所」には使えるが、「人」には使えない。
「訪ねる」はある目的があって、わざわざ行くというニュアンスがある。
Let’s tag the @Mods and see what they say
@vaer-k You should probably email them at hello@wanikani.com about your concerns. They don’t monitor the forums at all times, so emailing is best for feedback about Wanikani’s content. 
FYI, I sent an email to them referencing this topic, since I wanted to give some feedback on other items as well. So if you didn’t send them one yet, no need to do it now I think .
Thank you for bringing this up! We’ll take a look at this and see if we need to change what we wrote.
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