That's true. Part of the problem is that for the smaller woodwinds, the right thumb is responsible for holding the weight of the instrument. When a clarinetist is playing an open G, no keys are depressed, and so the instrument is supported only by the mouth and the right thumb.

The reason the left thumb has so few (saxophone and flute each have one, clarinet has two, oboes have one or two, bassoon is an anomaly) is because it usually operates the register key, which has to be held down much of the time while the other fingers do most of the work (not unlike a shift key for typing capitals). Having the left thumb do this is much easier than, say, the pinky, since you lose a lot of dexterity in your ring finger if the pinky has to stay depressed.

Some less common instruments do have more thumb keys; high-end bass clarinets have an extended low register and the two additional notes are operated by the right thumb. Bass clarinet typically uses a peg or a neckstrap, so the thumb is freed up a little bit to do some work.

(For a moment I forgot the main topic of the thread was computer keyboards and thought you had very strange piano technique!)

Interesting; so it sounds like rather than ignoring how thumbs work (like computer keyboards) they choose to take advantage of the thumb's superior strength rather than its flexibility.

Right. It probably also has to do with the fact that it's optimized for speed. The thumb is flexible, but not particularly fast. Many of the thumb keys on the bassoon are for notes that aren't played often, or alternate fingerings that are more in tune than the standard ones, and can be swapped out for other fingerings when speed is required.