> Second, if this were true, the number of innovations would have decreased after we became globally connected.
It is not only about "innovation" but about cultural diversity. For good or bad, a globalized world is standardizing culture around the world. Hollywood was a very powerful starting point as allowed everyone to see what the USA produces.
> innovations spread very quickly
That is the point. There are less and less pockets of different approaches. In one side of the world someone invents a new app and people is using it in the other side of the world 3 days later. Innovation may be fast, but it is not diverse but there is a convergence of ideas and ways of thinking. If we get it right it is fantastic, if we get it wrong there are no alternatives.
A good example, hot topic, is cryptocurrencies. If it is something good they are everywhere, if it is a mistake then it is consuming an incredible amount of resources for no use. If you had pockets of innovation the impact would be smaller and it will take more time to copy it if it becomes successful.