What about programming your remote from your desktop without having to install programs and drivers? And the producer not having to develop software for various operating systems? (Windows, macOS, Android, iOS, Linux...).

Think about timer switches. Setting up the timers with your phone is easier than on the switch itself. And it's probably cheaper to produce.

It's just too bad Apple has turned from an early adopter to a slow follower regarding Web API's which makes it harder for manufacturers to go the Web Bluetooth route.

Why not?

WebBLE supports GATT read and write. BLE does have an HID mode, but the primary way you are “supposed” to access BLE is via GATT transfers.

You could absolutely do a remote control right now. You would be at the mercy of packet interval timing (7.5ms-50ms depending on agreed interval) so gaming keyboard wouldn’t be great typical use could absolutely be done... but guess what, HID mode still has a minimum packet internval timing at 7.5ms. I’ve been using BLE for years but still haven’t found a great use for HID mode.