Input not recognised when using Switch Control remotely
I found out myself and I hope it'll be useful to other people. I don't think this has been done before.

You need to use BetterTouchTool to assign your remote input to the local trigger you want to use on the target machine, then go into BTT's preferences and tick the box "Always use the old keyboard implementation" in advanced keyboard settings. Now you have it, Switch Control will finally recognise your remote input and transmit it to your iOS device.

Couple that with QuickTime's ability to display a USB wired device on the target machine, and you can now 'remotely control' that device using ARD or any other Mac-to-Mac remote control app such as iTeleport or AnyDesk. Of course Switch Control is very clanky way to control an iOS device, but at last it's now finally possible!

Thank you Apple for making my life a clanky hack joy. Next time please make an ARD that directly tunnels to iOS.