What is the best history that we can imagine?
What would have happened if (fill in the blank)?
How different could things be?
Robert Heinlein imagined a future society where magic works like a technology - a flying carpet transport company must pay compensation to a church because the flying spell ceased to work above consecrated ground - and Poul Anderson, more consistently, relocated this magical technology idea to a parallel Earth. SM Stirling imagined maybe the worst possible scenario with his Draka. I have noticed a further possible motive for writing alternative history fiction: wish fulfillment, not so much "How might we build an optimal society now?" as "How might this world have been a better place all along - even though it wasn't?"
It is logically, and maybe also quantum mechanically, possible that there is an indefinite number of alternative Earths with unpolluted environments, multiple Atlantic Oceans with no trans-Atlantic shipping lanes or air routes, innumerable opportunities for lucky cross-time travelers to make a fresh start and get it right this time. This vision, plus the retro social setup of New Virginia, is a large part of the appeal of Stirling's excellent Conquistador.
Anderson was perhaps too realistic to present such a wish-fulfillment scenario. His Eutopian cross-time travelers seek the Good Land but then conclude that it is to be found only in the many imperfect worlds of their experience.