Most stuff now will happily access the first thing that connects to it while in pairing mode. I have many devices that a switch my headphone pairing between with ease.
The best pairing experience is with devices that have a pair button or let you hold down the power button to enter pairing mode. Although I've now ended up with headphones (Creative Zen Hybrid (Gen 2)) that have this, but also decide to just unexpectedly enter pairing mode when you disconnect all devices from it...
Apple has a proprietary USB protocol for pairing its own wireless keyboards, trackpad and mouse, and Microsoft and Sony have proprietary protocols for their respective gamepads.
However the protocols to do that are all proprietary and mutually incompatible. At least the PS3 protocol has been sufficiently reverse engineered so you can plug a DualShock 3 controller into a Steam Deck and have it just work wirelessly afterwards.
> I wish they would give you the option to pair through USB. Just plug in the host and peripheral and press the pair button, and it should automatically negotiate pairing.
This is called "Out of band" (OOB) pairing and supported since Bluetooth 4 iirc, it's a method which allows key exchange using a different bearer than Bluetooth.
It's implemented quite famously on the Sony Playstation 3 and 4, where BT-pairing is done by connecting via USB and pressing the "Playstation" button.
On other Bluetooth-devices it's mostly not implemented because apart from the limited support for OOB pairing over USB on the host-device, it would require the peripherial device to also have a USB data-interface in control of the Bluetooth chipset.
So more complexity and cost, to solve a problem which barely exists anymore.
The spec. allowed to exchange encryption keys with a different method than Bluetooth, Sony is using it on the Playstation to perform BT-pairing via USB.
Commercially, NFC was mostly used to initiate pairing, by having a NFC Tag on the accessory which stored the Bluetooth address, and a device scanning the tag would initiate pairing with the device directly.
The pairing itself is technically still done over Bluetooth, which is nowadays mostly a matter of confirming the operation...
You'd go up to the speaker (which you had to do anyway to turn it on), and you'd touch the phone to the NFC part. That would turn it on and pair it with this specific phone. The whole thing took less than a second.
It was great for sharing the speaker among family members, when different people used it at different times, each with their own phone.
This was in ~2015, I had a Galaxy S4 at the time, no idea whether this works with iOS or modern Android.
My biggest annoyance with Apple devices is in software, that AFAIK there's no way to prevent macOS from pairing to any Apple Bluetooth device connected via USB, even if it's already paired with another device and you only intend to use it via USB.
AFAIK, PlayStation wireless controllers are Bluetooth-only, but the DualSense (PS5) controllers use some proprietary extension not supported on Windows for haptic feedback over wireless that's sent via standard audio protocols over USB.
I think maybe there's like on one or two people who have gotten neard daemon doing Bluetooth OOB with Bluez, but it's very obscured in results or their reports have bit rotted off the net.
You can try an Android App like NXP TagInfo to read the contents of that Tag and show you what's inside of it, my expectation is that it's just a basic NFC Tag...