Control vs power.

I use both a "power" mawashi-geri and a "snapping" mawashi-geri, depending on what I am doing. The controlled, snapping method is fast and stings to be hit with but doesn't usually have much penetration unless you kick with the ball of the foot. That said, it is very useful as a set-up in sparring or to quickly snap a strike into an exposed target, and it can be very distracting. The more committed, more powerful method obviously penetrates more and hits harder than the snapping version, but it also tends to be a bit slower. If you want to cause more serious damage/pain and you aren't terribly worried about missing or having your leg caught, it's a great option.

It's always situational with such variations of techniques.  If you only want to disrupt someone's balance or break up their movement then speed and targeting are more important than power.  Breaking someone down physically requires more power and with better set up to connect with the target.  When it comes to the particulars of the round kick, you can pick your targets as well.  To the thigh or ribs, if you are landing with the shin and not the ball of the foot, you need more power to inflict any real damage.  The inside of the thigh and the head are viable targets for a faster, more snapped round kick. 

As to not being able to stop the kick if you miss, let it pull you through and develope the foot work to either take an angle and end up out of danger or steal a page from the Thai boxers and let it carry you around.  Learn to shield and lift the oposite leg as a check. 

I'd like to ask more about Mawashi Geri. Up until I took up Taekwondo I'd learned this kick many times but always kicking with the dorsum of the foot and always with the knee-raise-foot-pivot movement. Then I learned to kick with the ball of the foot (which I call Mawashi Koshi Geri and love putting into SP-10 above the knee). I also learned an arcing/lateral movement . One of my studets who is Dan graded in Shukukai has learned this latter movement but also to use the dorsum of the foot as the striking surface.

The kick doesn't appear in any kata that I'm aware of. My understanding, and this is where I'd like validation or correction, is that the kick was invented by Gichin Funakoshi's son whilst a WWII POW. If this is true it would explain a few things, like why it's not the kata, which were devised years previously but is in TKD, which came later. Also this is around the time that "sport Karate" was coming to the fore and so this kick is a sports kick, not a pragmatic kick. Although, as stated, I do like a ball-of-the-foot version to the knee, below the eye line.

Sorry, not sure I understood the question, but in TKD its mostly taught with the ball of the foot for board breaking reasons. in sparring we use the instep and lower shin.

I know that in Isshin-Ryu they use the kick in their kata and call it a squat kick (o toshi geri).  In which you step offline laterally and then bring the leg knee up to do the kick.  In Uechi ryu, they use a roundhouse kick with their shins to kick each others legs as a form of conditioning.

But, you are correct that in Goju-Ryu and Shorin-Ryu there are no roundhouse kicks.  From what I have read, it was Gichin Funakoshi's son that introduced the roundhouse kick into what later became Shotokan.  If we look at the purpose and set up of the kick, it is a great sparring tool but if we put it into the context of a civilian self-defense system we can see why it wasn't included in the older katas.

As a side note, I have heard that it was/is used in the older chinese systems and may have come from there.

Also, the debate of control vs power makes me wonder if any of the 'feats' of skill where by masters show great cntrol have any purpous other than a party trick? I mean we have all seen people punch really fast and pull it just touching someones nose, but all that means is that it was so unpowerfful they were able to stop it with minimum force. As martial artists, we should be trying to develop max power, not minimum.