Interior doors in America

It's because we don't use the metric system

So when I take my morning dump the stench wafts out from under the door to share with the rest of the household.

It's honestly something I've never noticed or considered.

I think it could be because most houses are made out of wood. So there will be settling, and the wood may swell and shrink a bit depending on the weather. So if there isn't a gap the door could get stuck.

There isn't always a large gap at the bottom of the door, but when there is, it's probably for clearance over a high-pile carpet.

https://toolsowner.com/gap-size-under-door

This article gives some important reasons for it. Besides door swing space and accomodating uneven floors, it seems air flow and furnace efficiency with HVAC cooling/heating systems are an important factors.

I always thought it was due to carpeting on one side of the door. Make it too low, and it'll drag on the carpet. Make it too high, and someone can peek in.

One reason is for modern air conditioner systems to work correctly. In a return air system the entire home needs all air to cycle back to the unit through, in most cases, a centralized duct. The larger the gap under doors the more efficient that circulation will be.