Great question @Neil7! I think the concern with cross draw is possibly flagging an innocent person.
One thing we should all do is train to defend from a seated position. We may have to use it - in church, in a car, at home if someone bursts in and we’re seated.
Check out these threads for some ideas on training from a seated position:
You may have already seen them, but a refresher never hurts! 
Glad to have you here, @Neil7!