Family member has just arrived in Berlin to find that non of the checked bags made it on board. But amazingly it seemed to take two hours from arrival to find this out. It was my understanding that the aircraft can't go anywhere until the crew know the weight of the cargo. In which case they'd know on departure - and passengers could be told then. Or at the least immediately on arrival.
Not exactly clear from the OPs post. Are we saying that none of the family members checked bags made it on board or that none of the checked baggage of any passenger made it onboard? Those are two very different scenarios.
If it is the former - none of the family members bags made it - then I would ask what was their flight itinerary. Was this a connecting flight with a tight connection, so they made it but their bags did not? If not, when did they check in? I ask these questions because while it is still the duty of the airline to inform passengers, there are solid reasons why a bag may not make it. Especially in busy airspace where you're dealing with slot times. Waiting 5 to 10 minutes for connecting or late check-in baggage can mean the difference between making your slot and waiting 2 hours for a new one. Given the amount of money that could potentially be paid out in late fees should the airline wait, you can't blame them for going without. It is often the difference between making a profit that flight or not. I firmly believe airlines should not be selling tickets with connection times of less than three hours. That's a good buffer for delays, security, and getting to the new gate. I strongly urge anyone not to even purchase a ticket with a one hour connection - that's simple begging for trouble.
As for the second scenario, I doubt highly that all the checked bags for the flight were left behind on a Heathrow-Berlin sector, although it can happen on longer flight segments. That sector is too short, unless they were holding Moscow as an alternate. I just don't see that happening.
Now on to informing passengers. I've done it before, but all that happens is because I don't know whose bag made it (I'm told weight and bag count, but not whose bag made it), everyone is panicked. Then they're not listening to the safety information, or they're giving the flight attendants a hard time through the flight, or they begin arguing with each other. This could result in an unruly passenger situation where we're landing somewhere else to kick someone off. That's not good for anyone, and only inflames the situation further. So instead, it is better from a flight crew perspective to wait and let the gate agents at the other end deal with it. Yes, it sucks. Yes, it can be seen to be very poor customer service. And I agree: it is. But we don't have the tools to fix the problem in the air, so it's best not to make it a problem, especially when we often find this information out after we've closed the main cabin door and pulled the bridge away from the aircraft.
In that light, I do think this is something airlines need to fix yesterday. We certainly have the technology to track bags and inform passengers through the airlines app. There would have to be new procedures written for what to do if a passenger says their bag is not on board, but I can tell you that I'm not holding up a multi-million dollar show for a single bag, especially where there are slot times or weather concerns involved, so the solution needs to be in the app itself. A simple "my bag didn't make it" button that is processed by the airline by the time the aircraft lands. If it turns out the bag did make it, all is well. If the bag didn't make it, any payments are immediately refunded and the airline begins the process to return the bag, with a maximum amount of time between when the flight left and when the bag is returned. And by maximum, 3 to 4 days on a sector that is served hourly is not acceptable. Rush delivery next available flight (not airline specific). Heck, that's a whole new revenue stream for airlines - connecting lost baggage!