FWIW, I'm not sure I've ever actually encountered that in my entire life. It seems like one of those folk tales governments tell when they want to get more money out of a group who are an easy target. After all, can you prove you only charged that nice couple what you said on your accounts for fitting out their new bathroom, Mr Plumber?

A professional tradesman invoices after and then accepts a bank transfer.

Sure, and when we've had tradesmen in that's almost always what we've done too.

But again, in my entire life, I don't think I've ever received a paper invoice from a cleaner, or a gardener, or a neighbour's teenager who was childminding, or the friendly retiree around the corner who is an ace at fixing bikes. Not unless they were working through an agency and it was the agency handling the billing, anyway. Not everything is big enough and formal enough to need invoicing and professional payment tools. Normal people still pay for plenty of stuff with cash around here. Just not usually in shops (online or bricks 'n' mortar) or for big things.