Frayed seatbelts won't pass an MOT in the UK. (Don't know about any other country).
Get a plate from US state that has no inspections? You need no inspections at all!
You can't put foreign plates on an irish registered car without first bringing it out of the country and registering it abroad either. I don't think there's any tax due on re-importing a car that's already been registered however. (you even get the same plate numbers since they're consistently mapped 1-to-1 VIN-to-plate forever)
I 100% oppose these inspections, and fully supported the initiative to remove them from my state.
Cars younger than 3 years or older than 40 years ("historic vehicles") are generally exempt. If your MOT isn't up to date, your insurance is invalid.