My Asus board has two pairs of USB3 and SATA3 controllers as well, Intel and Asmedia. Perhaps they utilize both to prevent potential incompatibility issues, to provide options as their speeds slightly vary or maybe one or the other doesn't support the appcharger feature, etc... I have no idea, to be honest. I used to think USB was USB... now one has different USB controllers and different SATA controllers, HD Audio and Legacy AC '97 Audio... let's just make things more complex. Now I have two volume icons in the tasbar, it's ridiculous... I'm probably going to dump the fatty Realtek HD one. I don't want to make my music sound like I'm in a church or concert hall. Just give me some quality, clean, basic audio without the fat.
I prefer to skip the unneeded drivers as well but when it doubt - install. CIR is Consumer Infrared, ie if you're planning to utilize an infrared controller as depicted in your manual p. 34
ftp://174.142.97.10/manual/Z77%20Extreme4.pdf
Some basic info on Intel's Rapid Start and Smart Connect:
http://www.intel.com/content/www/us/en/ultrabook/ultrab...
I'm quite sure I skipped the Rapid Start driver on my Asus, I read it isn't as beneficial when you're running an SSD - and my system is very responsive when awakened. Smart Connect seems more geared towards laptops as well but I suppose one could benefit from it based on one's needs.
Here's some info on the Lucid driver:
http://www.lucidlogix.com/product-virtu-mvp.html
That's not one to skip.
I'd install the rest though, including the SATA3 driver you mentioned. It's either in there because it's required to function, or it's updated.
On another note, I skipped a serial port driver on my Asus because I don't need it. But now it's being flagged in my device manager, lol... which is bloody annoying too. So I'm going to go ahead and add it. I'm no expert, mind you... I don't know if skipping drivers has any potential negative side-effects affecting other systems. This particularly applies to the VGA driver. As you're probably using a dedicated GPU, you may not need asrock's VGA driver. Heck, it's huge... 150MB! But does that in any way affect the performance of your GPU or Lucid? No clue!