Destroying something that a full drydock has to replace is much better then killing the carrier completely.
Let's say (for example) you've got an Escort Carrier working with a Marine Detatchment in a system that's defended by a CV. There's no way the Escort Carrier can defeat the CV. But there are reinforcements on the way for the Marine Detatchment, whose goal is to sieze a nearby planet. A surgical strike from the Escort Carrier renders the CV blind. Since it dosen't know what the Escort Carriers target is, and it can't detect them to intercept them or engage them, it withdraws to friendlier space to re-build it's radar. In the meantime, before it can return, the Marine detatchment secures the target and reinforcements arrive to hold the new target against the CV.
Also, in Secret Ops you fly multi-stage strikes where you eliminate turrets and shield emmitters. If you also eliminated the carriers Radar it wouldn't know when you were coming back with your force until you were in range.
Also, in our example of the CVE and the CV above, with some careful planning the CV could eliminate the Radar of the CV and if it remained in system, work it's fighters hard to pretend to be a full CV wing. Since the CV couldn't detect it, the CV wouldn't really know what it was up against, giving the CVE more time to operate and making the Cv more wary (if it's captain knew what he was doing).
Let's assume also that the new missile is a fast (or faster) then an image rec missile, with the long-range addition. You approach an awacs to find that it's escorted by two to four light fighters. Your part of a strike, in a bomber, and you don't want to engage because your configured for a Wild Weasel load out, but you carry the new missile, you dump it at extreme range, and turn and run. The missile homes in by itself, instead of being a FoF which might home on something else, or having to wait for a lock with an image rec, or instead of engaging two to four light fighters in a bomber, it homes straight in and blows the hell out of the AWACs craft, freeing up your strike force and not requiring anything more then a bomber.
Also, you assume that each gun turret and missile turret has it's own built in targeting radar (which must be the case, since the missile for eliminating those batteries is designated the HARM missile) but I don't think that would always be the case. In fact, I would stress that it is probably not the case. Most turrets and capship weapons would probably rely on the ships radar and sensor array for targeting data.
You see the same thing with Vietnam SAM sites (which is the closests example I can think of) where you have 3-5 launchers attatched to one or two radar devices. Also on modern US warships, the missile launchers do not have their own radar systems, the Missiles themselves do, but they do not activate until they fire. Aiming is accomplished by use of the ships main radar, which is more powerful and can detect targets at longer ranges.
Also, as in the US fleet today, I do not believe that an AWACs ship would ever be lumbering around un escorted. Carrier Captains in the US Navy always protect these craft as if their life depended on it. I don't think complete Air Superiority is possible without an AWACs craft, making them indispensible to whatever forces emply them. I wouldn't send one up without at least 2 fighters covering it, and I would feel better if it had 4, personally. But these are just my thoughts and opinions.