By the way the standard ISO 668 intermodal container has a total limit of about three tonnes; the unusual, heaviest size is about ten tonnes. A container port won’t be prepared to handle anything heavier or even, in practice, the 10 tonne version. These constraints apply to the rest of the system (roads, trucks etc — they are “intermodal” after all) so anything outside these constraints (wind turbine planes, major ship engine blocks etc) isn’t containerized anyway.
In other words the point of containerization is to be able to ignore these distinctions. If you care, you ship as if it weren’t in a container
If a shipping operator can eke out a few extra percent of efficiency by taking container weight into account, they will try to do so.
Of course, they will have to balance the efficiency gains against extra complexity.
But it's not so different from eg Amazon taking what's going on inside the AWS VMs into account when deciding on how to run their data centre.
Eg you might have booked a VM with four cores, but if you are typically only using one, they'll take that into account during placement.
The actual ISO 668 limit seems to be 30 tons.
You need to do all this just to massively increase the complexity of your billing model to offer slightly different rates of insurance. I'm sure there are teams looking at ways to make this better (just stipulate in the contract that any super valuable containers arrive early so they're loaded lower), but this is a HARD problem to solve completely.
Same for the rest of what you describe: yes, a perfect system would be a lot of hassle, but making any effort at all is sure to yield benefits.
You don't need to change the billing model necessarily. The customers don't have to know that you are doing this kind of optimization.
Of course, the more you can expose incentives to your customers, the more efficient you can get.
But even if your containers arrive in arbitrary order and you have to make your decisions on where to place them 'online', ie before the next container arrives; as long as you have any choice left at all, you can try your hand at optimization techniques.
Also, consider that from the point of view of the people loading the ship, it's all insured. And if you didn't get the insurance then you understand the risk. Why would they care? They aren't the insurance company. What's their incentive?
The same effort is better invested into making sure you are not losing containers.
It's like saying 'we can optimise policing so that stabbings only happen to the right people'
Even “Even spread” would be a serious topic of debate - Even spread over what? Geographic area? Residency? Where people are likely to be at a given time? Those are three radically different answers in any commuter city.
My guess is that the orchestration of how containers are loaded is complex enough that the order of stacking is best left up to the shipper and adding cost/location optimization to the equation might make things too complicated. The containers should be loaded in the manner that is the safest and most efficient for unloading.