Why do citation styles for webpages include accessed date?

A URL does not refer to content, it is only an address. Since you are making a claim about what was written at that address, you must associate a date with it, or it is meaningless.

If you do such a thing, you should also save the content, in case it is not recoverable and you want to refer to it again or support it further.

I am not aware of any published accounts of how style rules are developed. If you really want to know why a particular rule was developed, you need to asked them directly. That said, there are a number of different styles for dealing with electronic materials and these styles are changing:

• MLA: You always need the date of access for electronic resources.
  • At some point the since 2014, the requirement has been dropped: https://style.mla.org/access-dates/
• APA: You rarely use the date of retrieval, although in previous versions (APA 5) you always did
• CMS: You never need the date of access/retrieval. I am not sure if you ever did in earlier versions.

If you know the URL and date, you may be able to use The Internet Archives (a.k.a. the Wayback Machine) to see the page, if it didn't change too frequently.