Well, AirPlay is designed for casual mirroring to a TV, not for connecting primary monitors. It only supports up to 1920x1080 currently, and it does that far too slowly to be workable for anything other than static images (because of a low refresh rate).
AirPlay simply wouldn't work for higher resolutions. And forget about gaming.
You would need 'such a big bandwidth' because that's simply what modern monitors require to function at their potential.
A resolution of 2560x1440 at 60Hz, which could be considered fairly standard today, requires a bandwidth of 5.9 Gbps. I'd like to see the wireless interface that can reliably transfer at those rates... Not to mention the bandwidths required by 4K and 5K displays. A wired external interface to support 5K resolutions (DisplayPort 1.3) has only just come out and haven't even made its way into any actual products yet. Existing 5K monitors are having to use two cables to get a 5K signal. How might one expect to do wirelessly what currently requires two cables of the fastest wired connection standard available (DisplayPort 1.2)?
If AirPlay mirroring is sufficient for your monitor needs, that's all well and good. It isn't for everyone else's.