Have we finally reached a point where the number of people with access to scanners and email is great enough for a business to justify not accepting faxes?
The problem with this is that there is a wide range of technical sophistication "out there". You may have a scanner and find it a "no brainer" to scan and email paper originals, but don't make the mistake that everyone falls into this category. Fax (as a stand-alone device) will eventually go away, but it will be around for many years to come. For many, the ease and convenience (and decidedly "low tech" requirements) of a fax machine is just too appealing. As to how this relates to your decision, get a low-cost Internet Fax account. If you prefer to scan and email, you can do this, while still providing a way for those who wish to fax to do so (and you get the fax as a PDF file in your email). It also gives you the option to scan and fax, when you encounter someone who can't or doesn't want to receive your scan via email.
Depends on your clientele. If they want to use one then you need to have one. I wouldn't make you're not having a fax machine a barrier to your customers. You can get multi-function printers pretty cheap these days so there isn't much of a cost.
The above being said there is no reason you need to advertise the fact that you accept them. Just be able to say yes if someone asks.