Why didn't Manticore join the Solarian League?
Because they were too smart to submerge themselves in an SL whose cracks were already evident to them, mainly. They had the best of both worlds (at least until the RoH went off the rails and became the PRH). As things stood, they had (in no special order):
(1) proximity to the core for what they wanted from those worlds;
(2) plenty of economic opportunity (Manticore & the merchant marine) from the SL economy without SL bureaucrats;
(3) (relatively) corruption-free politics (again, until the RoH went off the rails);
(4) a very lengthy tradition of independence;
(5) the status of big fish in relatively small ponds rather than a few more minnows in a vast ocean;
(6) no desire to invite OFS in while they were busy being OFS locally (the RoH after it went off the rails).
In theory, the SKM could have sought SL membership to hold the PRH at bay, but their estimate of the situation was that the SL was little if any better than the PRH (remember how widely the Manty merchant marine penetrates the Shell and the Verge; Manties knew the reality behind the SL facade entirely too well) and that they had a pretty good chance of standing up to the PRH by themselves. It is remotely --- remotely! --- possible that a sufficiently desperate SKM might have sought League membership/protection if it had turned out that the PRH steamroller couldn't be stopped, but by that time Manty opinon of the Sollies was low enough (remember how few positive impressions of the League you've seen from a Manticoran perspective), that they probably would have preferred to either go down fighting or else make the best negotiated terms they could with the PRH.
Manties like Beowulfans and vice-versa; Manties do not like Sollies, and they draw a clear distinction in their own minds between Beowulfans ("their" Sollies -- you know, the good fellows next door whose families we've been marrying into for the last couple of hundred years) and the rest of that wretched mass of rotten, smug, imperialistic, slavery-enabling, platitude-spouting-but-not-honoring, free-trade-inhibiting, oh-so-superior bastards in the League. [G]
By the time the PoH had gone thoroughly off the rails, the only membership status it was likely to find in the SL would have been as a protectorate writ very large, although its locally produced elite might have been able to cut a deal with OFS to become the local tax-collectors, but Manticore lay between the League and the PRH, and you can be damned sure the SKM would never have stood idly by while the PRH signed up with the SL and the SKM (which knew how much the League was just salivating for the chance to take over the MWHJ) found itself between the "main" SL and a brand new SL lobe which used to be called "Haven."
Looked at in the most positive possible light, Manticore had no more interest in joining the League than Canada (or even Mexico) has in joining the USA. Looked at in a more reasonable light, the SKM had no more desire to join the League than Finland had to join the USSR (or maybe even than Cuba, under present management, has to join the USA). And any extension of the SL into the Haven Sector would, in effect, have had to come through Manticore because of the Junction.