Those of us that can reel with both our right and left hands are just better than those of you that can't. (just kidding)
For me personally, I like to palm the reel on baitcasters. In order to do that I have to change my hand position no matter what side the handle is on. So, for me, casting with my right hand is more comfortable and accurate. Casting right hand and reeling left hand would still require me to change the position of my right hand on the reel. I would have to throw the bait out, grab the handle, or something with my left hand, then reposition my right hand in the palming position. It would be a fairly awkward thing when my entire reel and rod is supported by just my left hand on one paddle of a handle.
Now, when I use a right hand retrieve, I cast out with my right hand, then grab the reel in the position I want with my left hand producing a hand to hand transfer and not a hand to handle transfer, which is much more secure for me.
With spinning gear, I don't need to palm the reel, so I cast with my right and reel with my left. I've never had any problem setting hooks with either hand on the rod, but I prefer casting everything with my right hand.