It works only if you use each peripheral with a single device, and never switch. For example, I have a decent over-the-ears Bluetooth headset. I like to use it with my work laptop, to listen to music, with my home computer, for VoIP, and with my phone, for making phone calls. Re-pairing takes ten minutes of restarting headphones, reconnecting on the computer/phone, and repeating until the stars align and the devices recognize each other. For a wired connection, I would unplug from one device and plug into the other.

If Bluetooth pairing could be easy, then it might be a replacement for wired connections. Until then, it is a highly situational protocol.