While trapeze-based travel systems sound cool as hell, I'd maybe look at a few other items:
- Are these nations monolithic? Are there any factions or people who can be pitted against each other? Are there political parties within a nation, for instance, who could be manipulated into a civil war or a coup? I've found that the more factions (and sub-factions!) you have, the more fun intrigue becomes as a pillar of play. Keeping them straight can be a challenge, but it's quite rewarding, especially when your players start linking a faction in Country A with a heretical sect in Country B in order to supply arms to revolutionaries in Country C. Or they just burn it all down. That's cool, too.
- Are these nations all equally lawful? You don't have chaotic evil orcs, but do you have bandit gangs? Elven death squads killing journalists for an autocratic regime? Manticores who enjoy disemboweling their prey and then playing jazz trumpet to entertain the target while they bleed out? A gnomish Manhattan Project? A church full of life clerics who kill some of their acolytes every year to ensure scarcity of clerical healing, thus commanding higher rates? You can do a lot with groups of people who either don't conform to or actively subvert archetypes.
- Finally, to actually answer your question, it's very much dependent on group. Hell, sometimes it's dependent on the day - if someone's had a terrible week and they are not here for complex political machinations tonight, it can really crimp things. You can still run a group of murderhobos in an intrigue-heavy setting, though. For an example, look at how you would run a murderhobo group through Eberron or Ravnica. That's where you can really leverage intrigue or political actors as patrons for the party, and the murderhobos start to look like highly skilled mercenaries or retainers for a lord, who tolerates their disruptions because darn it, they're just really, really good at their jobs.
This is awesome, good on you!
I'm curious - why can't you have chaotic paladins? I mean, how else would you characterize Ancients or Vengeance Paladins (assuming you're playing 5e here; if I'm wrong, let me know).