Remember, there are two types of insurnace you want to make sure you have: 1) liability (which covers any damage they do to your property or other sub's work and 2) worker's comp (which covers them if they or their employees get hurt.
You need both for each contractor.
And, I am quite sure that if a sub or a sub's employee gets hurt on the job, the GCs worker's comp coverage will only cover them if THEY hired them. If you, the owner hired them and they don't have their own WC policy, then it is on you.
Liability experience - a welder scorched a ton of new wiring in a renovation. The wiring was low voltage and couldn't be spliced so had to be totally redone. The loss was in the tens of thousands (this is a big rehab). His insurance covered it. Had it not, do you think little ol' welder guy would be paying snooty low-voltage guy for his smokin' wires? Not on your life.
You have to have insurance or it WILL catch up to you one day.