My understanding is that the tradeoffs are:
1. Weight
2. Cost
3. Lack of user serviceability.
It definitely seems like a good tradeoff in some circumstances - particularly in rainy environments.
My understanding is that you can't maintain the hub shifter at all. It's sealed so it's generally pretty low maintenance, but if/when it eventually breaks you have to send it to the factory for repair.
The internal gear hubs have been perfected before derailers even became a thing; it's a very mature tech.
You can[1] do some maintenance on them. I don't have any experience with that, as all my internally-hubbed bikes were stolen long before such a point :-) :-(
One big tradeoff you missed is efficiency. The belt drive is efficient, but internally geared hubs are currently less efficient than traditional derailleur setups. Losing watts to drivetrain loss is a major reason that internal hubs are not as popular with human powered bikes. The durability and maintenance need to be WAY better to get someone to switch over.