Recall that violence within a CCS safehouse is not public knowledge because the CCS knows that it isn't legal (despite the Government/CIA backing). The initial publication blurb notes that they're basically intended as an extrajudicial hit squad and political Designated Enemy--basically, they're the evidence that "[Jerks]", as my Nightmare Mode game called 9/11, just might be a Government plot in LCS-world.
Even under C+ Police Regulation and Death Penalty (where the Death Squads are), the CCS is beyond the pale. I don't think there's any way to publicly justify the Government or the CIA having both the justice system and the Conservative Crime Squad.
IMO the primary downside to the Backer List CCS-kill is that it doesn't leave the CCS safehouse(s) available (they disappear or never exist), nor does the LCS get the 200 Juice bonus for killing the last safehouse. If you plan on using a lot of Sleepers, bumping them all to Urban Commando (and thus, being able to recruit additional sleepers) can be pretty powerful.
So far as I can tell the optimized solution is to get the list early, publish it, kill the first two safehouses, and milk the last one for Juice and combat XP. Once the first paper comes out (arresting C+ legislators and moving Police Regulation to L, both of which are very nice benefits early in a Nightmare game), you've got 4-6 months to kill the last safehouse, but you do want to kill it yourself.
If the FBI raid actually did go to all three CCS safehouses, well, they'd have caught my seduction squad at one and my hackers at another, each reasonably well-armed & armored and with non-attached LCS members present too. The CCS was holed up at the third. Making the raid actually hit LCS-occupied safehouses would be one possible way to make it less advantageous for a violent LCS. Whether sleepers anywhere could provide notice is a separate question, but I'd hope that someone (possibly military or CIA sleeper) could issue a raid warning.