An alternative reading of " - We Also Walk Dogs" (see here) is that, despite being listed in the Time Chart and despite being included in a Future History collection, it does not really fit into Heinlein's Future History. Its newly invented gravity control technology is not mentioned in later stories where it would have made a difference. It refers to seven extra-terrestrial races in the Solar System whereas other Future History stories mention only two: Martians in "Ordeal in Space," Venerians in "Logic of Empire" and both in "The Green Hills of Earth." Further, these Martians and Venerians seem unlikely to engage in the kind of interplanetary power politics suggested by " - We Also Walk Dogs." The story mentions Luna City but a lunar colony of that name could exist in almost any future involving space travel.
Because the Future History is a series, not a serial, most of its installments could be read and assessed separately. "Common Sense" is a sequel to "Universe" and "The Man Who Sold The Moon" was written as a prequel to "Requiem." The latter, about Harriman's death, would have remained a valid story even if Heinlein had not later added the longer account of Harriman's earlier career.
If " - We Also Walk Dogs" is read separately, then it need not be seen as leading to the worsening political conditions of "Logic of Empire." Instead, its protagonists look forward to profiting from the application of the "O'Neil effect" to space navigation, colonization and recreation. One comments that, "There's always money in giving people what they want." That sounds like a utopian future for all: the public gets what it wants and their suppliers get "...gobs of money..." in the process. In practice, of course, many members of the public might not be able to afford luxury items and a market economy can be guaranteed not to expand indefinitely but we still seem to be looking at a brighter future than the one described in the ensuing episodes of the History.