I really do hope the PS4 Slim gets a DisplayPort output and FreeSync. I can't imagine it would be hard to do. It might not be considered worth it given the lack of people who connect their PS4 to anything other than a TV, but couldn't Sony drop a line to the TV manufacturers early on in the PS4 Slim development process and let them know what they were doing? Then they could get on to adding DP and FreeSync to their next line of TVs, probably with some kind of PS4 Slim Ready/Smooth Gaming/etc. branding.
DisplayPort on TVs and consumer electronics like games consoles is not likely to happen, in my opinion. There will be a handful of TVs with a DP, but mostly it is not important for manufacturers or most customers.
These interfaces exist for a reason and are designed to best fit the devices that drive them and the display panel used in the product.
DisplayPort is a computer connection and like DVI and Analogue VGA before it, can be implemented free of charge. But, its direction is influenced by the computer industry and computer manufacturing industry.
HDMI is controlled by a consortium of interested parties that make consumer electronics and there is a royalty fee to implement it in your product. It also has the support of many big content producers that influence its direction with regards to its suitability for media consumption. Why add the cost of another connector when HDMI is entrenched and does what they need?
Lastly, and most importantly, a display with variable refresh technology is not simple to make. The properties of the panel itself are vitally important. The huge majority are manufactured to operate without artifacting at 60Hz alone. For variable refresh to be worthwhile, the panel and the electronics that drive it, must be able to deal with what happens when the refresh rate changes.
If you research FreeSync monitors right now, you'll learn that there are problems with the image quality in variable mode. These problems partly stem from the choice of panel and components by manufacturers and partly from the lack of a mechanism to uniquely alter the voltage to the panel pixels. It's completely possible to do this without a hardware module. You can run a shader on the GPU to take care of the calculations (I think it involves the prediction of frame times), but the problem with that approach is that the GPU has no idea what the panel's properties are (no two panels will be completely identical).
The other guys (Nvidia) involved in variable refresh desktop displays have chosen to solve this problem by providing a programmable module to display manufacturers. This allows the manufacturers to tune the module's behaviour to the individual panel and avoid the artifacts that occur when the refresh rate changes. I believe Nvidia also have some kind of panel selection criteria that display manufacturers have to adere to. This is a kind of work-around for the varying properties of panels and the vast array of manufacturers and quality control practices.
With the module, Nvidia can say; 'if you want to create a product around this tech, you have to follow these guidelines.'
Without that module and using technology that's based on a standard that's free to implement, what we're seeing so far is that AMD can only suggest the best course of action and the display manufacturers can basically do whatever they want, to varying degrees of success.
Eventually, the display industry might learn to sort this out themselves, but holy shit are they historically slow to adapt.
Of course, Sony is quite uniquely positioned to make all this happen with the PS4 and their own TVs. But a further question remains; is it worth it when most games on the platform target 30 fps and probably feature triple-buffered output?