Amex has a once in a lifetime rule for each card and now they are getting even stricter. But there are still a lot of cards you can go through if you do them in the right order between the business and personal cards.
But there is still Chase, CapitalOne and Citi. The Chase Ink Business cards you can churn as much as you want and most of the other cards have either a 24 or 48 month rule
Getting rewards that vastly exceed the costs is still very possible in the US. The days of “I travel first class internationally for free every few months and change cards as often” are long gone though. That pattern is trivially recognizable and most of the better rewards card providers will reject folks with that history even if they have perfect credit otherwise.
In the UK you can still cancel and re-apply after 24 months. It used to be 6 months but those good days are long gone...