That would defeat the biggest advantage of the covers.... they work in Pre-boot. Microsoft offered a Bluetooth attachment but it didn't sell well enough and has been discontinued but is still available online.
I use a BT keyboard for my work system and it works pre-boot as our drives require a bitlocker password to even boot.
As for the Type Cover, my take is wireless would be awesome in a very similar form factor that charges from the SP3 wen they are both plugged in. There is flex to the keyboard but I am not a heavy typer so it is minimal for me. I do not mind typing on when I am traveling. I do type a lot as I am a lawyer and constantly editing documents and I don't mind using it at all, though I did at first. I do love my BT keyboard, but I wish there was a better option from Logitech or someone else that allowed fast swtiching between devices and not just a small form factor like the 810.
I also did not pay $130 for it, too high IMO as well, I ordered mine from for $60
Amazon and it was used like new, still in the box. I think it should be bundled and allow the user to pick the color at checkout, or maybe just bundle at the MS store and for certain levels.