As compared to, say, Guns, Germs, and Steel.

I'm looking for a book or handful of books that will summarize the historical period without making glaring errors. Obviously a summation of such enormous breadth will have errors by omission, but I'd rather not read something that actively spreads false information. I'm not even sure what I'm looking for, but as an example, it might discuss the differences in aqueducts and their use across the several cultures that developed them in antiquity, whereas if I looked at Roman history, I'd learn about Roman aqueducts, but could stay completely ignorant of their use in Petra.

Anyhow, in the general section of the recommended reading, Why the West is at the top, but in googling it, I found this review: https://www.theguardian.com/books/2011/jan/30/why-the-west-rules-ian-morris-review

In brief, the review is quite critical, and suggests that Ian Morris ignores cultural and philosophical differences. Two paragraphs:

It follows that the reasons the west rules for now are to be found entirely (his word) in brute, material forces. To understand the evolution of the human species, all we need is a grid to measure progress, and Morris has invented it. The "index of social development" comprises energy capture, organisation/urbanisation, information technology, and war-making capacity.

...

And after all, we non-archaeologists can get sentimentally attached to the soft parts of history – faiths, values, culture – in our belief that they have something to do with being human, and can resent attempts to downplay their role in favour of impersonal forces.

So, again, what makes Why the West Rules recommended reading, when it apparently has such faults? Or if it's no longer recommended reading, what book(s) provide a good, readable introduction to the ebbs and flows of connected world history?

edit: I suppose I should note, for recommendations' sake, that I'm more interested in late prehistory through the 17th or 18th centuries than anything post-industrial revolution.