Curious Pax - The problem with your scenario is that it presumes similar circumstances for every aircraft in the system which needs to divert. Your Heathrow-bound widebody represents a quite different proposition from a LBA-bound B738 or a BLK-bound C56X. The notion of a smooth-functioning one-size-fits-all policy does not apply. You need bespoke solutions. You need dynamic case-by-case decision making.
Let's remember too that the era of mass diversions away from the London TMA airports due to fog is very much yesterday's problem. Technology advances have taken care of that for the majority of contemporary commercial airliners. And advances in flow control keep many short-haul flights on the ground at point of origin to calm traffic flows if they're planned into a fogbound destination airport. These days, a diversion is far more likely to take the form of an E190 which can't take the crosswind at LBA, an executive jet which can't get into a smaller airfield, an aircraft burning through its reserve fuel as it awaits a runway reopening following an incident (previous landing aircraft birdstrike, tyre-burst, etc.), or perhaps a technical diversion. Diversions take many forms.
Now let me offer another perspective. You are on an approach radar position and you have six additional aircraft which should have been out of the way on the ground by now, but which are instead in the hold awaiting weather improvement or diversion. You also have other traffic which would have been in the system anyway, so you're much busier than usual. And any aircraft which needs a diversion / reroute requires lots of additional coordination, because it is deviating from its original flight plan. If three of the holding aircraft are C56X's and the other three are B77W's, you will be very grateful if a nearby airport agrees to accept the C56X's, as in a radar environment each of those smaller types represents the same workload as a B77W. In that situation, you really want the largest airport in your area to pull its weight and pitch in. Manchester, almost uniquely, routinely declines to do that. MAN is notorious across Europe as the most frequent offender in this respect: "The airport that likes to say NO".
Yes, the aircrew perspective is important. But so is that of ATC, ground staff and everybody else. It has to be a team effort. It is so easy to take account of the protestations of one cog in the system alone. We also need to be mindful of safety considerations in flight, as well as those affecting operational convenience on the ground.