Utility of Fax over Email when both are available

A really big reason are signatures and laws. For example in some countries you can just fax a signature while using digital signatures would require you to get an official digital signature (usually stored on a smart card, if it exists in the first place, and sometimes having less "validity" than a handwritten signature), then get a smart card reader, install middleware which may or may not work with the program you wish to use to sign the document, and then the receiver may also need to have program which will work with the digital signature to confirm it, and so on for the whole chain.

It's not uncommon for some businesses to need to submit signed documents to dozens of different government regulatory offices, agencies, banks and so on and in all of them everyone will have to be trained and equipped to use the digital signature. Such preparations may be made on a level of single country, but what happens if you get a signed e-mail from another country (when the signatures are even more important because the other person can't just come over and sign a document himself and mail takes time and money).

Also the whole process of sending authenticated mail is a bit complicated. For a simple office clerk, it's often easier to just use fax, and then focus on doing the job he's supposed to do.

So basically the main reason is inertia of the society. Everyone needs to get used to e-mails, and almost everyone is already used to using a fax, so transition isn't easy.

Another problem is how difficult it is to access documents. Using a fax, you can easily send handwritten notes, or take a document and underline it by hand and so on. On computer such "simple" things are a bit more complicated. For example, if you have a document on the computer, you'd need to print it, do editing by hand and then scan it, or edit it on the computer, and people often aren't as used to interfacing with computers as they used to interfacing with a pencil. Also, mice are difficult to use for drawing and graphical tablets aren't often a part of standard office computer.

Faxing official documents with signatures and stuff like that just makes it easier for people at the receiving end. They don't have to go through printing tons of papers, instead the fax will take care of it AND will display your fax number at the top (for easy organization).

I don't think that fax has any significant advantage over email other than this. In the foreseeable future, you might able to have a type of 'email machine' where companies would have an email server with a special email for each department. Every email received would go through filters to remove any kind of spam and only accept legitimate emails. The machine would then catch these emails, send them to the 'email machines' of the department in question and it would be automatically printed off.

I don't know if something like this exists, but it's kinda cool :)