I'm minded of a discussion from
Handbook: Major Periphery States, dated to the early Clan invasion era:
Here we thought we're the ones on the frontier - staking humanity's claim to the deeps - and all along we've been living in civilization. Kinda like thinking you're living on Lastpost and then waking up one morning to find you built your house on Kathil.
Of course, that very segment includes a counter-argument against this, but there is a broader point to be made: if their goals included escaping the influence of the Inner Sphere, the founders of the four "classic" major Periphery states didn't go out far enough. Given their respective locations close to the burgeoning Great Houses, it was inevitable that the various powers of the Inner Sphere would brush up against these smaller domains - and that, as the Reunification War amply demonstrated, it was still all too close to avoid notice once the Spheroids were so minded.
Unfortunately, the largest known Deep Periphery power (outside of the Clan Homeworlds) has been caught by its very presence in the coreward sector. But the rimward, anti-spinward, and spinward sectors remain free of Homeworld Clan interference, even if the largest Deep Periphery states in those sectors do not compare to the Hanseatic League in terms of size, capabilities, or regional influence.
For most of the
ISP3 planets and powers, the most pressing dangers are domestic - what happens once the last Axumite JumpShip breaks down, when the next Upheaval breaks out within the Alexandrian Covenant, whether the New Delphi Compact ever finds a cure for the Curse... and whether or not such a cure might have unintended consequences for the NDCCS' attempts to patrol and protect the Compact's member worlds ffrom pirate predations.
While Interstellar Expeditions (the organization) does provide a window of exploration for those groups operating out of their various host planets, one coul argue that the only true way to escape the turmoil of the Inner Sphere is to take the plunge and head further out into the black... so long as you avoid heading into the coreward sector, at least.
However, if you choose to stay in the near Periphery, you'd either have to be both inoffensive enough to avoid foreign adventurism and lucky enough not to be in the way of anyone who'd go after you just for being there (or, in other words, be the Rim Collection); or be in a state large enough to be noticed (like the Magistracy of Canopus) and face tougher decisions on how best to deal with the cards you're dealt - and to handle those being held by your various neighours.
Also, it may be worth noting that not everyone in the "modern" Periphery buys in to the same narrative as those seen in the former Territorial States. The Marians, for one, aren't shy about carrying out their own conquests, and nor are they reluctant to subject Canopian and other captives to slavery. But from a gaming perspective, one could argue that they bring something different to the table, given how differently the Marian Legions are organized relative to Canopian or Taurian regiments.
(Technically, the Marians weren't the first Periphery state to be founded with less than modern ideals - Hector Worthington Rowe's Rim Worlds Republic came replete with helotry. But while those purported Platonian principles were phased out as the RWR matured, the Marians don't seem keen to discuss abolitionism any time soon.)