Hey, Hoss, how are you? As far as reel construction, back in-the-day all baitcasting and spincasting reels were right-hand crankers, and most spinning reels were left-hand cranks. Don't know why... just the way the manufacturers offered them to us. There were exceptions, as mo65 points out with the Mitchell 301. Penn also had a few right-handed retrieve reels in their line-up back then, but for the most part, you took what you got and lived with it. As it's been pointed out, in modern times just about all spinning reels (and many spincasting reels) are ambidextrous. Personally, I started out (as many of us) with a Zebco 33, which was a right-hand cranker, and when I decided to try spinning in the mid/late 1970s, I just couldn't get used to left-handed cranking (pretty much just the opposite of your experience). I just preferred to cast, then switch hands so my dominant hand's free. I finally settled on the Shakespeare President II 2810DE spinning reel, and just forced myself to get used to the configuration. Taught myself to cast left-handed, too. I'm glad I did, cuz there were times when one or the other hand was incapacitated, but I could still fish. IMHO, everyone should learn to crank with either hand, not only in case of hand injury, but also because it makes more sense if you fish two rods at a time, as I do. If both rods retrieve on the same side of the reel, and you get a bite on the rig you aren't holding, you have to set the rod you're holding down and grab the other one. With cranks on opposite sides, you can immediately set the hook while setting down the other rig, and greatly improve your chances of success. Setting a hook successfully, just like a lot in life, is a matter of timing. So if at all possible, I strongly recommend acclimating yourself to cranking either way.
BTW Barresi, there was an ambidextrous baitcaster out for a very short while. I don't remember the model, but Shakespeare put one out back in the early 1980s. Apparently it wasn't very successful, because it disappeared from the market in short order.
Tight lines, guys.