: Actually, scratch that. The original timeline says that national governments
: fought each other in space: The Jovian Moons Campaign escalated tensions,
: as Earth's national governments-many of which sponsored colonies within
: the system-began fighting proxy wars off-planet. As these proxy wars
: continued, tensions on Earth mounted, leading to a number of armed
: conflicts on Earth itself.

My interpretation of that was that Russia had backed the Koslovics on Mars as a way of ousting a US presence, and then realised it had created a monster when they kicked Russia out as well. My impression of the Frieden was something similar, with a German corporate consortium trying to get rid of their competitors and then being horrified that the mob they'd formed didn't especially want them either. That the whole thing started as an economic, rather than military, colonial proxy war between Earth powers that devolved into a true interplanetary war. I doubt international competition would have simply stopped by that point, whatever the level of hostility between powers is, and especially when you have a new stage to gain national prestige and economic benefit from.

By its nature, a proxy war doesn't mean sending your own troops against someone else's troops - it's sending them against people your enemy is supporting, and supporting someone your enemy is fighting. Like Russia backing the Vietcong, or the US backing the Mujahideen. So I doubt you'd see US, Chinese or Russian troops fighting each other, which gives them political room to eventually still band together to put down the shared threat of colonial independence.