From experience here ....I took over a small rural PC who was responsible for a village hall. ALL postal mail, most of it t to do with the running of the VH, was addressed to the former clerk. It took months to change over names and address and she was alive, goodness knows if she'd been deceased. I transferred all Council correspondence to the VH address. As already stated most stuff now is digital. However, out Borough Council still uses the postal system.
The parish were I'm Cllr uses the Church as its postal address. It's a small rural Parish with very little post Mail. It works well. Other alternatives I've heard of are a PO box address but this would incur costs.