If we look at the lot of them as I do (from the standpoint of a gunsmith) all were made in the days before modern high strength steel alloys.
The "weakness" they share is from the fact that they wear out and they mash out in use over time, and could not be made to work with pressures that we commonly use today or the "wear' was much accelerated. Their frames were all made of very soft steel.
With all that said, I will point out the other side of the coin.
If a modern gun company were to make one today and use the steels that they have available today, the break top design would be just fine, and could be used in all but the most powerful shells available. (I think they would be impractical for the long 500 and 460 magnums, but I could be wrong)
If we look at the steel of a Freedom Arms Casull, (17-4 Stainless) and see what kind of pressure it’s able to handle in stride, and were to use such steel in the frame of the top-break revolver and it’s lock, any shell up to and including a 44 magnum would be easy enough to work with.
Look for example at the locking area available on a top break design. The actual locking surface of the latch and frame could be about the same as the surface of contact in some bolt action rifles. If the hinge pin were made of sufficient size and the lock also made to cover about 3 square centimeters, the strength would be all we could ask for.
Look at the hinge pin in a Ruger #1 Rifle. It’s very strong. It’s not huge however.
Look at the total square locking surface on an AK47. Again, it’s quite strong, but the total surface is about 2.4 square centimeters.
Design is not the problem. Higher strength steels would cover the bases easily. Demand is the problem. So far, there has not been any.
For an outdoorsman I believe the break top revolver is a very fine design and not too bad as a fighting gun either. I cannot say it’s any better than a side swing cylinder but I don’t think its any worse either.