Both my previous landlords’ agents handed me such forms. I never once sent it in, but set up the standing order through online banking (for avoidance of doubt: That was pre-Monzo). I can confirm that neither agent complained about any lack of confirmation or other communication.
I don’t think the supplier can send it to your bank: (1) Are they really expected to have physical addresses of all banks in the country? (2) you need to sign it.
As for cutting off references:
Indeed Barclays also always used to cut off my reference for the rent payment after x characters. Never had a complaint from the landlord or their agent, but also never understood why the agents wanted such long references if they are not supported by the infrastructure …