What is the use case for Fax links in a webpage?

Computers, mobiles and tablets can send fax's with software, its just like sending an email, it was added to rfc2086 15 years ago but it never took off and as far as I know no major browsers support href="fax:" they do however support href="tel:" that can be used just the same to send a fax using software.

2.3 "fax" URL scheme

The URL syntax is formally described as follows (the definition
reuses nonterminals from the above definition). For the basis of this syntax, see [RFC2303] and [RFC2304].

  fax-url          = fax-scheme ":" fax-subscriber
  fax-scheme       = "fax"
  fax-subscriber   = fax-global-phone / fax-local-phone
  fax-global-phone = "+" base-phone-number [isdn-subaddress]
                     [t33-subaddress] [post-dial]
                     *(area-specifier / service-provider /
                     future-extension)
  fax-local-phone  = 1*(phonedigit / dtmf-digit /
                     pause-character) [isdn-subaddress]
                     [t33-subaddress] [post-dial]
                     area-specifier
                     *(area-specifier / service-provider /
                     future-extension)
  t33-subaddress   = ";tsub=" 1*phonedigit

The fax: URL is very similar to the tel: URL. The main difference is that in addition to ISDN subaddresses, telefaxes also have an another type of subaddress, see section 2.5.8.

You can just provide a link with GET variables to a third party pay-as-you-go fax service (i.e. like paygofax.com) that allows GET variables to populate.

For example:

<a href="https://www.paygofax.com/?name=John%20Doe&company=ACME&fax=4255559999" target="_blank">Send It!</a>

Full disclosure - I am the creator of paygofax.com as part of a "learn to code" project that I now maintain commercially.