It's not all that much.
For example, CD quality audio, uncompressed (lossless) is about 1.5mbps. This is the same as SD quality video.
Bump that to 96Khz and it's up to about 3Mbps.
Bump it further to 96KHz 24 bit and it's about 5Mbps. Still well within easy reach of an LTE connection; that's about the same as a 1080p stream on YouTube.
Add in some lossless compression like ALAC/FLAC and you shrink it down a bit, too. Lossless audio compression actually gets MORE efficient as the sample rate goes up because there's more redundancy in the data.
As for only Apple headphones being compatible, this has less to do with trying to be anticompetitive and more to do with the fact that bluetooth standards don't support lossless audio. Apple is able to do it by extending the protocol beyond standard Bluetooth because they're designing the hardware. Your typical Bose or Sennheiser cans are going to use standard Bluetooth where you're limited to SBC, AAC or AptX, all lossy codecs.