That states only under 12 months though Onyx. So once they're 12 months I assume they are supposed to just sit in a seat with a seat belt??

I do want to point out that there are people who do the wrong thing & they do sit with their child on their lap, & if anyone reading this ever does it for what ever reason DON'T SHARE THE SEAT BELT. In the event of an accident you could crush your child. If for God knows what reason it must be done, have the child on your lap, out of the seat belt.
I'm not condoning this in any way, but I think its something that people need to know.

I've only ever used a taxi needing a seat once when DD1 was 5 months old & it was provided. It was also reversable. I didn't take a car seat on the plane with me, but had DD3's with my luggage when we travelled. Car seats etc are free to travel on planes.