"They could do the light-touch only strikes at ridiculously high speeds, though"
That they can. Shotokan guys are usually extremely fast and accurate, with very good formal techniques.
It is just that they dont train for them to be used with full contact, and that they expect a umpire to call "break" when they hit, no matter how badly, in sparring.
There are exceptions to this ofcourse.
Especially in japan they do much harder contact (even if KOs still results in disqualification). But even there they still only do one-hit-break sparring.
The caricature of a shotokan point fight is tho guys standing almost motionless for a minute, then they jump towards each other and one guy gets the first light touch hit, whereupon the match breaks up and is returned to start position.
The caricature of a kyokushin/knockdown karate fight is two heavy muscular guys leaning forehead against forehead, trading body punches and lowkicks -without much attempt at blocking or evading, until one suddenly takes a quick step back and throws a high kick that scores a KO.
Neither of these are entirely true, but there is a grain of truth behind them.
A few kyokushin (actually two kyokushin and two kyokushin offshot) fights:
http://www.youtube.com/watch?v=qMMUpYsvR9c
http://www.youtube.com/watch?v=lUdSsH1doK0
http://www.youtube.com/watch?v=BIS7JC1Uuak
http://www.youtube.com/watch?v=4d_dDgedvkU
(no fancy KO highlights though, more complete fights)
JKA (shotokan) karate clip:
http://www.youtube.com/watch?v=ufh6B-r_HOM
http://www.youtube.com/watch?v=u4R-4xjpaCQ
As you can see, there is a big difference.