> What would be needed is an intervention force that takes over the entire country and stabilizes it
An occupation force is not tenable in the modern era.
Per a Washington Post article from 2004[1], the post-WW2 occupation of Germany had an initial force ratio of one occupying soldier per 40 civilians. At that level, occupying forces could assume direct command of civil structures, without needing to sign deals with the least-bad bandits or warlords in waiting to act on our behalf.
Per Wikipedia, Libya's current population is a bit above 7 million. With a similar force ratio, that means an occupying force would require 175,000 soldiers. A Fermi estimate of cost is $100k/yr/soldier ($10k doesn't pay for salary, $1m is implausibly large), giving an occupation cost of $17.5bn/yr[2] before any special funding like (re)building major infrastructure projects.
This kind of cost is insupportable in a modern democracy, where voters will rightly ask why 'we' should bother. Libya was not and is not an existential threat like WW2-era Germany, and we're not in the imperial/colonial era where occupying forces could loot the country to pay for its own occupation.
[1] -- https://www.washingtonpost.com/archive/opinions/2004/05/09/a...
[2] -- This is also why meaningful intervention in Haiti will not happen, if you believe the calling-for-intervention reports that civil government has more or less collapsed in that nation.