While it is certainly possible, it's worth keeping in mind that Bluetooth has a greater latency than a hard-wired controller.

But i see that there is bluetooth midi interfaces, so if you now can hook up any midi device "with midi ports", i am not sure the extra work having the device with built in bluetooth? When you just can plug in these bluetooth midi controllers into any device or?

Wireless connectivity can be useful in situations where dangling wires would be a problem. For example, in a live performance scenario.

Sure could be, i am not sure if i missunderstand you but there already is standalone ones? So maybe actually doing the design with a built in do not add much? Well maybe convenicence.