Some headphones support connecting two devices simultaneously, which is great... unless you have 3 devices :)
Anyways, if I was Apple, I would have added paired headphones to the speaker menu.
You can’t do this with a regular Bluetooth audio device that doesn’t have the W2 chip, because according to the Bluetooth spec, you can only be paired to one device at a time; there is no separate concept of “known” devices; devices that auto-connect stay auto-connected on sleep+wake; and devices that connect (therefore devices that auto-connect) must stop announcing themselves as available over BT discovery. (BT is essentially a protocol state machine — a device can be either idle, in pairing mode, searching for its paired device to auto-reconnect, or connected, and none of these states can overlap.)
These are all limitations of the audio device, not of the host OS. Limitations required for Bluetooth conformance! Apple can only work around these limitations by having the device and host both run a completely separate, second discovery protocol over completely separate hardware, that just forces the BT hardware into certain states as a result of its own negotiation. They can’t magically make audio devices that don’t have a W2 chip do this out-of-BT-band negotiation.