Lots of assumptions and not enough facts here.
I don't work for BA, but in my company, like in many, lots of people commute. I am myself a commuter, even if the place I live is just one hour and a half away from where I work. I've done the round trip for paperwork yesterday leaving around 10AM, back home by 4.30 PM.The majority commute from places not very far away (same country or bordering countries), some from far away: I've met people living in the US, Canada, Thailand, Africa etc. It needs lots of planning but it is entirely feasible. Usually people get to their base the day before their "on duty" flight, or anyway several hours before in order to get some rest and to allow plenty of time in case you get stuck somewhere. Some then get a hotel room (all hotels around airports have airline staff fares, starting around 30€), or a B&B, or have a crash pad, or a friend where they can bunk.
There are many ways to make sure you get where you have to go. You can buy a "seat available" staff ticket if the loading factors are good (you can check the loads on the company site), or spend a little more for a staff ticket with a booked seat if the flight looks full.
In the end, people commuting are not more tired than the ones living near the airport. You can live 2 miles from the airport and show up for your flight having partied the whole night. No one can make you get the required rest if you don't want to. In the end, it is up to you to know your limits and respect them, which is what CC and pilots usually do.