Old School games necessarily tend to take place on the fringes of civilization. The center, the heart of any civilized territory, is a place that has no need for adventurers... right?
In order to address this question, we'll have to look at several subjects, starting with exactly what adventurers even are. Only once we understand what drives the need for adventurers in the generic (or this case, specific, 10th Age) fantasy setting will we be able to decide whether or not they have any business being in the so-called center or whether they should be purely relegated to the boundary lands and liminal outliers.
The Defining Attributes of Adventurers
Well, in a purely gamey sense, we can say that adventurers are anyone the players want to play, but that wouldn't be quite true, would it? If the players decide they want to play farmers with a realistic farming simulator it can be done (not with D&D, or at least not with any rules that I have on hand) and they would hardly be adventurers. So what separates adventurers out from the pack? I've talked about this a little before when I said that adventurers are rockstars. But what I really mean is that adventurers are outsiders. Of course, I've spoken of adventurers as insiders as well, but this seems to be a departure from the norm.
The defining attributes of an adventurer appear, then, to be:
Social Mobility and Swords for Hire. This two things together generally make adventurers a type or class of mercenary (and in my games they are treated as almost identical with mercenary companies and mercenary soldiers). Certainly, the second part of that equation may be dropped, but that severely limits the options for the PCs. If they aren't for hire, they are most likely working permanently for a single paymaster or patron, which means they do what he wants when he wants it. Nothing like receiving orders from an imaginary man all the time to make your players feel like they're in a straightjacket. Not that it can't be used to good effect, every once and a while. (See something like the military campaign proposed in the Fighter's Handbook, or a real military campaign in-setting where the PCs join up with some army).
What drives the need for adventurers?
In order for adventurers to serve, there must be a need for their services. In a standard fantasy world, this is most likely because there are: (1) no police forces, (2) no standing armies, and (3) no well-trained elite soldiers. Certainly you may have knights and leveemen and even, if your setting is semi-Roman or just historically inaccurate, something approaching a police force. But these things don't have anywhere near the level of institutional strength that they possess in the modern day. There will always be gaps.
This means the drive to hire adventurers comes from an inherent weakness in the pre-modern model of civilization. Someone must be on hand to troubleshoot the institutional flaws: these people are, in the fantasy setting, adventurers. They can serve as makeshift police much better than a squad of knights, fight like an expendable army, and eventually become an elite squad of murderers that can dismantle entire bandit encampments and goblin armies all on their own.
Does this need exist at the center?
Well, if your adventurers are insiders, this question is irrelevant. There are things to do other than fulfill the need for adventurers. You could be a lord, a priest, a politician, someone engaged in the tricky every day business of governing. But if your PCs are actual dyed in the wool adventurers, the answer is: Yes.
Even stable kingdoms are not monoliths. For example, someone always hates the king. There are always problems. There are bandits, outlaws, political rivals, street gangs, merchant compacts that must be investigated, foreign spies, enemy armies, and a general level of crime. No kingdom has complete control over all the territory in its borders, and it could always be more secure. Sure, those insecure places resemble the liminal outside adventurers normally inhabit, but they are deceptively close to society itself. The slums in a great capital. The forest nearby. The road between this barony and that one. All of these are "insider" places, places that are not part of the "center" but are directly adjacent to it.
And what about political intrigue? Ahh, this is the real meat and drink of the center. For all these nearby liminal places, the real damage is always done by intrigue in the heart of hearts. Nobles scheming against one another, houses locked in ancient and bitter rivalry, kings desirous of consolidating control over their independent lords. Lords who would be kings, or who would foment war.
Do adventurers belong in civilization? Well, the civilized folk may not think so, but it seems there is just as much work there as there is on the fringe. Adventurers don't need to be shunted off to some wild outside. Let them come in once and a while, and taste the danger of the city, the settled kingdom. In fact, some of the more memorable adventures are likely to happen there. While it's all very well to fight goblins and orcs, let us not forget: Man is a wolf to man.