The safety of the children would have been one reason to stay in the UK. In the UK (and in many other monarchies) there is a code of honour between press and the family. Especially where it comes to the children. In the US they are much more sitting ducks. There is no codes of honour between celebrities and the press on that side of the pond.
Meghan says she would never be able to bring Archie to school, while in reality Kate and William drop off the kids plenty of times. There is only a scheduled press moment at the beginning of the new school year.
Here in the Netherlands it's even less, the royal family has the agreement for the first day of their level of school (no idea how you say this in English), when they start the lowest grade, then high school and when they start university. Besides that there are two portrait moments a year, and the rest of the year they are only pictured when they are at engagements. Seeing a picture of our queen shopping or whatever is extremely rare.
Yes, the British media has a different relationship with the royal family, but there is still some sort of respect. Let's remember, the sitcom The Prince was an American invention, not British.