Well the idea is that the Colonials convince Kerensky and his fleet to go back and at least save Earth the Terran Hegemony. This does several things for the Colonials.
What it does is it creates long term problems the Colonies could do without.
For the following points, I'm assuming the Colonies replace the Pentagon Worlds.
1.) It looks good and is a public relations coup for the Fleet. I mean helping to save Earth would certainly be a big win for them.
Save Earth... From
what exactly? Earth is in no actual danger, only it's political / economic / industrial domination of the IS is. And the downtrodden Colonies will see a
lot of parallels between how Earth exploited the IS with their own situation...
2.) It allows the more aggressive fleet elements an outlet to fight in such a way as to not antagonize the Cylons.
Depending if Colonials moving past the Red Line to re-link with reminder of Humanity will antagonise them or not.
Probably it would trigger a war, the Cylons would understand that they must strike now while they still can, or otherwise they'll be out-massed and out-tech'ed far too badly.
3.) Stabilizing the Hegemony ensures that Colonials have a very 'grateful' ally they can call upon later if and when Round 2 with the Cylons ever commences.
Gratitude will last maybe a generation or two. At best. Also, Earth people were very contemptuous over the IS folk, never mind some far off "Colonials". It would grate too much for them to live with the notion of "owning" some backwater yokels. Best
erase the notion...
Much more can be achieved by convincing Kerensky to settle in the Colonies and share / sell the goodies.
4.) Advanced technology and weapons to revolutionize Colonial society and the military ensures they're at least capable of defending themselves from some of the Great houses but also ensures they dominate against the Cylons in any real engagement.
With weapons and other tech from Kerensky, they can take the Cylons. They most likely could have taken the Cylons if not for the CNP backdoor.
Combining their space capabilities with SL tech,
while keeping their FTL from the IS, they can fend off any of the Great Houses, since these simply can't afford to spare the military forces and logistics to go after such a far-away target, as the GHs must look to their own borders first and foremost.
However, a Star League reborn
could spare the forces needed to reach and subdue the Colonies.
SL restauration is the worst possible outcome for the Colonies, as it's the one entity they can't hope to defend against. As long as Inner Sphere stays divided and fighting itself, no Great House can spare the forces needed to subdue the Colonies without critically weakening their strategic vectors.
Thus the Colonies can stay on the sidelines and build up / expand like mad.
5.) A Strong and recovering Hegemony keeps the Great Houses looking inward instead of outward towards the Colonies. This effectively has the job of keeping their focus inward. There is genuine worry that the Colonies would be gobbled up by one or several of the Great houses.
Until the next First Lord dusts off a tried and true speech:
"Furthermore, in consideration of the common goals we share, we must set aside our differences and pool our resources for the common good, once and for all.
The Star League stands for a unified Humanity. As First Lord of the Star League, it is my solemn responsibility to protect the welfare of that Humanity wherever it may be found, be it on Sian or Santiago, New Vandenberg or New Avalon, Andurien or Apollo, Castor or Canopus. Though me, the Star League assumes the awesome task of safeguarding the welfare of Humanity. It is a responsibility from which the League will never shrink, a responsibility it shall never lay down. The dark days of barbarism are over-we will not let them return again.
The only way to ensure equal protection for all, the only way to safeguard the liberties of each individual, is for every Human being to accept the benefits we offer, freely and openly. So long as a solitary individual of the most distant planet in the Periphery remains uneducated, impoverished, or disadvantaged, all are equally stricken.
We intend to see that the majority is not denied the benefits of culture and progress at the hands of a minority of radical isolationists. We intend to extend our benevolent protection into every corner of Human-occupied space, whatever the cost, until every man, woman, and child prospers and flourishes. Let no one stand in the way of Human progress. The time for reunification has come."
Bend over, Colonials. It's for your own good anyway...