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.
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.