Intel has branded wireless display as WiDi, Apple has AirPlay, Google has Chromecast, and now Amazon has entered the market. The value of platform lock-in is tremendous for these companies, so the incentive to move to a more open standard isn't very high. But how much longer can that be the case?
This isn't comparing apples to apples, with wireless displays the control has to be tighter since only one person can have control of the screen at a time (or perhaps a small subset of people) unlike WiFi which can handle huge numbers. Yet the principle is similar. A protocol to dictate who is in control as an admin, who controls the screen, how the bit rate and quality are negotiated, and more. This protocol isn't unlike the 802.11 protocols that dictate the security, handshaking, and data transfer for WiFi.
At work we plug into 1024x768 projectors with a VGA cable from Dell laptops. That sentence could have been written in the late 90s and would have been relevant... ouch.
I use AirPlay at home frequently. Many family members have Apple TVs that allow the same, but with Chromecast costing a third as much and Android sales booming, it stands to reason that cross platform wireless screen sharing is going to be in high demand soon*. Or are people (and companies) going to need to buy one of each? Google has gestured toward cross platform screen casting, but it is far from ubiquitous. What level of cultural adoption would be required for Apple to consider adding support for it at the expense of AirPlay?
I don't know how long it will take, but eventually something (probably) has to give.
*I know Chromecast is cross platform, but iOS limits the support to apps that build in support themselves. I'm talking about native system-wide screen casting.