Conceptualizing A Sequel

How might Poul Anderson have conceptualized a sequel to HG Wells' The Time Machine? I think that Anderson would have deduced new implications from Wells' premises. The Time Traveller had deduced from his observations (see here) that:

(i) The Eloi's ancestors conquered Nature...

- then added:

(ii) ...and their fellow men...

- then, finally, added:

(iii) ...but those fellow men's descendants are now in control.

However, these conclusions were derived from only a few days of observations and in only a single location, the Thames valley. Why assume that the entire Earth is in a uniform state? It never was in the past. We can assume only that the rest of Britain, Europe and the world enjoy the same paradisal climate and have, or have had, the same level of technology. From this set of assumptions, it is possible to imagine innumerable other societies on Earth in 802,701.

It is automatic for sf readers to ask whether human beings survive and thrive elsewhere in the Solar System or in other planetary systems (see The Time Machine And The Terran Empire) but, before that, we should ask about other parts of this planet. Has anyone looked at it this way before?

Is causality violation possible in the Time Machine timeline? Since Wells does not mention this paradox, I think that it would be inappropriate to introduce it. Any sequel should explore Wells' single imagined timeline. There should have been some space travel and also a rediscovery of time travel before 802,701. And, of course, we want to know what did happen to the Time Traveller.