(apologies in advance if this seems like a safety rant. I've cut and pasted a few items I've posted elsewhere over the past few days)
West & Ivo,
You both bring up good points...the most salient of which is
when the shit hits the fan it happens fast and drowning or getting injured can happen in a few seconds. And more often than not we are left to our own devices when on the water, even though we might be surrounded by our mates. As an instructor the weight of this responsibility is compounded by a student with little or no experience, and therefore caution and preparedness are paramount. Analyzing the situation and acting quickly is extremely important as well. A few examples when I've seen bad stuff happen was because the victim either was paralyzed by fear, injured/unconscious, in denial and refusing to ditch the kite, or not equipped with a knife a few times.
I've had to cut lines twice in 10 years. Once recently when another kiter crashed his kite over the top of my lines and his lines were all tangled up with my body/harness/bar. I tried for a few moments to untangle myself but the other kite was still powering and cutting my fingers whenever I tried to unwrap things - plus I was being dragged toward shore which was occupied by children and their families on a busy holiday weekend. I quickly decided to cut the other guys lines (sorry). The other occasion was as described above when I had to jump on someones lines while in a death loop...
There would have been a third and fourth occasion in the past 3-4 years/ once when a friend had his line wrapped around his finger, but it (his finger) was lopped off before I could get to him. The other was when another friend caught his lines on a crab pot buoy in high wind and waves and it was dragging him underwater - fortunately he freed himself but I almost watched him drown. Trust me this is a horrifying thing to see.
Another friend was dragged backward by his leash. He thought about his line cutter but realized that it wouldn't cut very well. (A few days later after he got out of the hospital he "bench tested the line cutter on his leash - it took over 10 seconds to cut under totally controlled conditions on dry ground). IMO the attachment point on harnesses should be on the front to minimize the chance of dragging backward. I suppose for guys doing handle-passes this might be inconvenient, but here's an example when you need to make personal choices.
Where to keep the knife and how difficult to actually use it? - I have a scabbard style knife with a combination blade (Gerber River Shorty - around $30usd) that is lashed to my harness on my right side (I am right-handed), but also in a position I can reach it with my left hand. I have a lanyard "daisy-chained") so that it will not get lost if dropped. (Actually during the second episode mentioned above I dropped the knife but was lucky it was tied on and I could still get it into my hand).
As mentioned before I am not a big fan of the "line cutters" they sell with some harnesses. They are better than nothing, BUT they will not cut thru a leash, at least not very easily, and the blades rust out easily. At any rate they should also have a lanyard. Plus they are often located in little pockets on the harness, sometimes on the back of the harness. Try pulling that out sometime when you are body dragging...not easy. There are some better line cutters out there that are probably adequate for the job, but I still like something with a real handle grip (personal taste)

Fumbling with any knife is not easy when the shite hits the fan. If you want to simulate it just go out in the water and start doing some kiteloops as you body drag and see what it might be like. Therefore it's hard to train for this sort of thing, but you should at least give yourself as much chance as possible by equipping yourself with something that will cut FAST and WITHOUT FAIL.
Even though I've only cut lines twice with this knife I am glad I have carried it for a long time. You do need to maintain a knife - I clean, sharpen, and grease mine 2-3 times/year. Any wise diver or parachutist will carry a knife to extricate himself in an emergency - why should a kiter not have one?
Also keep in mind that after a kite has looped more than 5 or 6 times the lines are twisted together like a rope with a lot of tension and the kite could be locked into kite-loop mode. It may not matter what typed of safety system you have at that point and you might be dragged until the kite hits something or a line (or kite) fails. Therefore you need to decide whether to QR from your CL AND from the leash.
The reason for a kite looping can be a number of things - bridle fouled/damaged, line caught on wingtip, line hooked on harness, leash clip fouling lines, etc...Sometimes it is resolved easily, sometimes not so easily.
I don't like to advocate releasing a kite unless absolutely necessary for several reasons, but there are times when it is the right choice. In most cases a released kite becomes fairly docile when it does not have the resistance of a rider dragging behind it. (Please don't misinterpret any of this - I do not want people to start slashing lines and activating their QR's without good reason)
some photo's of my harness/knife as mentioned above.
Dakine harness, actually has a small pocket that fit this sheath nicely. The Harness came with line cutter in a pocket on the opposite side.

Another waist harness with the sheath mounted on the straps.

Note in both photos the (daisy-chained) lanyard. I wrap a loose bit of tape to finish off the daisy chain so it doesn't unravel inadvertently unless you give a little tug. Also have tethered the sheath to the harness so it doesn't get lost, and also taped the belt clip shut.
Some people might not like having a knife lashed to their harness and worry about it poking into their ribs or something - not a problem for me after 1000+ sessions. I have had the knife pop out of the sheath on occasion while riding and it dangles behind me without any issues. I just pull it up and sheath it while riding. No biggy. Seems that some people are afraid of impaling themselves on the knife somehow, but I don't see that happening (not saying it's impossible, but highly unlikely IMO)
Sorry again for the long reply. Kitesurfing is an amazing sport and everything seems beautiful until there is a serious accident - and they happen quickly, seemingly without any warning, and in some cases they could have been mitigated or avoided by having the proper gear/safety eqt.