Optics are used for situation requirements. Carbines don't have to be limited to just close combat. A scope on a carbine is perfect if you need pin point accuracy and a lightweight more manuverable firearm. Just take a look at the Remington 700P with 26 inch barrel vs the Remington 700 LTR with a 20 inch barrel. Some applications require a more compact firearm, hence the reason for the modification to the Remington.
Since it's most likely for you to use your AR as a multi-role platform, such as close combat AND precision shooting, you should have both a long range scope and an optic for closer range, such as an aimpoint or eotech.
If you have more than one AR, you should make them specific to the role you want them used for, since your capabitilies are not as limited as the people who only have one.
The accuracy of a carbine is very decent comparing it to it's big brother with the 20 inch barrel. I honstly have never seen a significant difference until you get past 500 meters.