the Army CAN fly in red illum now (at least in OEF). They have a stand-alone FLIR for SA purposes (not tied to any 1553 bus/nav system or anything, and the display is mounted to the side of the dash (where the adjustment handle for the pedals is), and currently the O-6 accepts that high risk now by mitigating with FLIR and flying acceptable approved low-illum routes. So now we get the call mostly when it's crappy WX. And that bit us in the a$$ recently.
agreed with busdriver on how our assets should be used downrange right now. I'd like to not be sitting on my ass all the time, while the MEDEVAC bubbas fly multiple times a day. It's just not an efficient use of resources!
As to why EUCOM and PACOM have dedicated CSAR (that also deploys downrange, too) is because of the higher potential for bad things to happen in those regions. Technically, we're still at war with NK, and China's looming large as well. That's the sort of conventional cross-the-fence-behind-enemy-lines war that would fall precisely into our mission set. Then on the EUCOM side, there's always Russia, I suppose. That unit used to be based in Iceland and provide SAR for that country as part of a treaty agreement with the US back in the day. Now they do their own rescue (we trained them up sufficiently, just like we trained the ROKAF up as well), and Kef closed, so they moved them somewhere else.