I did a GEDCOM test using FTM v22.214.171.1243 and looked at the results in a text editor. The web links are not included, not when attached to people or citations. There are several places where it would make sense, to wit, under a custom tag or appended to notes. They're just not there.
I haven't really used web links except for testing, so I don't have anything to add to your suggestion. I do put links into source citations (into the detail field generally or via template fields), but I always create PDFs of any pages cited because I never know how long the links will be valid, and I don't want to depend on internet access to see source media. It's one of the reasons I don't anticipate using this feature much myself.
PS. *.doc and *.docx files are not supported on this forum. Would be nice if PDFs were though to facilitate sharing. Anyway, until these file types are allowed as attachments here, you can always share these file via free file sharing sites, your own website, etc.
PPS. (Aside) 捌 comes out in my UTF-8 export as æŒ when UTF-8 is supposed to be able to encode any character.