I have just built and automated 21 cruisers to check what assignments they get.
3 are patrolling mining stations (quite valuable ones. One is mining Loros Fruit, the others valuable luxuries).
13 are patrolling my home planet.
5 are patrolling other colonies.
It seems that they tend to be assigned to patrol more important assets than the smaller ships defend, but they still get patrol duties.
As long as you also saw smaller ships escorting to a higher degree, this supports what has been said - mure "valuable targets" for bigger ships.
The AI will always have to give an order as far as I know (freighters and exploration and a few more can be idle somewhere). So a military ship should have an order.
So pick your choice between repair, refuel, move to, attack, escape, escort, patrol, load troops, unload troops, and probably a few more. Patrolling a key colony is the "top AI defense mission" as I see it.
While my "top defense mission" would mean sitting parked on top of the colony (in the gravity well), doing nothing at all.
The good thing about the eternal "patrol" is that it ought to hang around, the bad thing is that they burn fuel. My idle defenders may be dragged away by some enemy visit, and will not be near the colony at a key moment. But when sitting at the wrong end of the system, they will at least not be low on fuel (I got collectors).