What is wrong with the content protection of AirPlay that some applications prevent its use?
Airplay isn't a protected transfer mechanism, in the same way that playing (for example) a Blu Ray disc over a HDMI connection that supports HDCP.

High-bandwidth Digital Content Protection (HDCP; commonly, though incorrectly, referred to as High-Definition Copy(right) Protection) is a form of digital copy protection developed by Intel Corporation to prevent copying of digital audio and video content as it travels across connections. These connections include popular ones like DisplayPort (DP), Digital Visual Interface (DVI), and High-Definition Multimedia Interface (HDMI)

The system is meant to stop HDCP-encrypted content from being played on devices that do not support HDCP or which have been modified to copy HDCP content. Before sending data, a transmitting device checks that the receiver is authorized to receive it. If so, the transmitter encrypts the data to prevent eavesdropping as it flows to the receiver.

That's pretty technical, but in short (and this is not particular a developer choice, but the content owners choice) if they cannot guarantee that the content is fully secure end to end, they will not allow it to be transmitted.  Airplay isn;t fully secure to the same degree as the above, and so many contents owners will not agree to it's use.