Software (including A.I.) developed outside of your culture won’t reflect your culture. We already see this problem with regard to racism and sexism — A.I. which cannot detect black people at all, or hand-written healthcare software which cares more about insulin than periods — so for example, if you leave it to America and China, you won’t have any education software (with or without A.I.) which can cope with the difference between a Gymnasium, a Realschule, and a Hauptschule.
USA companies are also already having a lot of trouble with the cultural difference between the “easier to seek forgiveness than ask permission” attitude they’re used to in America as compared to anywhere which enforces rules because they exist for a reason. Google Street View in Germany, for example. I don’t know about Chinese companies, but I assume they also have cultural assumptions that won’t apply outside China.
I'm not concerned on the consumer side of things. We're all part of a global economy. If you want to buy AI services in Germany you can do that easily, just as I can use Google without a problem despite Germany not exactly being at the forefront of the tech. Having Google or Facebook physically located in your country, from a consumer standpoint, actually doesn't really matter at all.
Honestly this whole arrangement has always puzzled me from an American perspective. Americans sacrifice quite a lot in terms of equality, privacy and so forth to be at the forefront of this stuff, and we can just use it all the same because we're good customers. I'll be sad the day the US decides it doesn't want to be in charge!