I was interested to see what other folks thought might be tweaked to support various viewpoints and sort out the contradictions. I am distinctly NOT of the opinion that there's a clear right way to interpret the setting and other concepts belong in some other game world.
OK, here's a way to interpret the rules, not necessarily a specific setting like the Third Imperium. This expands upon my "safer Points of Light setting" previously and brings together many of the ideas in these threads.
TL;DR: Because of the nature of jump drive, Traveller supports an Empire where 15-25% of worlds are important, the rest wilderness frontier, and these can be completely intermeshed within each other with no contradiction at all.
1) Star empires exist to promote space travel. Their territory defines the potential span of travel, but the territory is not necessarily fully settled.
2) Starports and Pop primarily define the importance of a world in a star empire. These are the worlds that will be connected by x-boats and couriers, naval and scout bases. Other natural connectors will be mains: strings of worlds within Jump-1 or each other. Together, this is both a lot of worlds and still a small percentage of total worlds. This is the main resolution of the contradiction: the empire IS the systems it chooses to connect, and without reliable jump drives or transport, the vast majority of worlds within the territory of Empire are hardly OF the Empire.
3) Let's quantify the math of 2). I'm using MegaT, which is close to CT and the intent of the original rules (we can riff on this later). The normal probability of a Class A or B starport is 5/12, and the probability of a Pop 8+ world is 1/6. The probability of both is 5/72 = 6.9% and the probability of neither is 35/72 = 48.6% (remember these rolls are independent in CT and MegaT), so somewhere between 7-50% of worlds might be considered important. Let's say 20%. So in a subsector of 40 worlds, 8 are important and 32 are not, and in a sector 128 are important and 512 are not, on average. It would be easy enough to establish Cluster/Backwater subsectors with more/fewer good starports (MegaT does this).
4) The results of 3) give us the following. Per 1000 worlds on average, 200 are High Pop/Good Starport, and 800 are only one or neither. 200 worlds is a lot of worlds, with a lot of Pop by definition and mostly good starports. Civilization! There is lots of travel and trade between these worlds. But there are 4 times as many other worlds with low Pop or mediocre or worse starports. The Wilderness Frontier! Scattered settlements of the widest variety possible: lone miners, religious sects, lost colonies, scientific outposts, pirate havens, disgruntled rebels, and on and on and on. But the resulting setup is relatively safe for Civilization, because the Wilderness Frontier has low Pop and probably low TL and resources. Low Pop is key: the Wilderness Frontier does not have the numbers to threaten Civilization en masse, though perhaps at points.
ETA: 4a) Low TL is a near absolute firewall for Civilization. TL 8- worlds can be completely ignored by the Empire in most cases, as they have no ability to engage in interstellar travel (or DO they...).
5) This is what I meant by "safer Point of Light setting." In a fantasy PoL setting, leaving the settlement is dangerous, and even the settlement may not be safe because you're surrounded by monsters. But in the setting above, it is easy to stay within Civilization without being bothered by the Wilderness Frontier despite being surrounded by it! So we now clarify what I meant by "weirdo Travellers": travel within Civilization is not weird at all, but travelling into the Wilderness Frontier sure is! Yet because of the nature of space and jump drive, the Wilderness Frontier can be completely intermeshed with Civilization, and Civilization can mostly ignore the Wilderness Frontier. This is what the Third Imperium ultimately did NOT do: it ultimately became mostly settled. This was a choice and did not have to happen.
6) Space is not land. There is no terrain to restrict movement. The only criteria for world desirabilty is distance and the world itself. It is quite reasonable to think that 70%+ of worlds are simply not worth the bother, at least in the initial stages of colonization. This justifies the 80/20 split above, but it also produces our first riff: we could and may be should adjust worlds for desirableness. So yes, if you roll a Garden World, up its startport and Pop. If you roll Pop 0 (planetoid belt) maybe you don't want it to have Pop 8+, and if you do, make certain it's TL 9+. I think Pop 0 Gardens and Pop A wastelands are crying out for explanation, but you can simply erase them if you want.
7) The Wilderness Frontier is RIPE for exploration for those crazy enough to go there! And you can always run back to Civilization to rest and resupply. 'Nuff said.