I have always though of a turn coordinator as a magnificent solution.....
to
a non-existent problem.

Do you call designing a smooth flying autopilot a non-existing problem?
True some later autopilots achieve smooth flying by tapping off the
attitude indicator, but I believe this is slightly more complicated.
I'll grant you that if it were not for the autopilot problem we would
all be happily flying around with turn and bank indicators.

If turbulence bumps the aircraft to a 30 degree bank but the aircraft
does not turn, the ball will instantly show this by moving toward the low
wing.

True. For that reason I shouldn't have said that you wouldn't even
know about the 30 degree bank until the turn started. I was thinking
from the autopilot's perspective. (The autopilot is not hooked to the ball.)

Since the ball does not over-react, the pilot won't either.

The turn coordinator does not over-react any more than the ball does.
It merely shows the sum of the yaw and roll rate. In any case the response
by the pilot to an unwanted bank angle whether detected from looking at
an AI, TC, or T&B is the same - enter a smooth coordinated turn in the
opposite direction (usually requiring both aileron and rudder opposite
to the unwanted bank) until the airplane is once again straight and level.

I've seen some pilots (esp. those relying mostly on a T&B) respond to
this situation simply by stomping on the rudder opposite to the direction
of the ball deflection. Perhaps the reasoning is - well since it is only
the ball that is out of whack because of the damn turbulence, I'll counter
the turbulence in the most expeditious manner by an equally jarring jab
on the opposite rudder. This works fine unless you have any passengers.
They will turn green about 3 times faster than if you fly properly.

The thing I like most about a needle is that if held exactly on the
standard
rate turn "doghouse" timed turns are very accurate - the kind of accuracy
that makes partial panel approaches practical.

Bill, you are showing your prejudice. It is entirely practical to do
such approaches with either instrument. On my CFII checkride I did a
fine partial panel approach down to 200 feet using my turn coordinator.
I've seen other pilots do this also.

As far as timed turns, remember that once the turn has stabilized
(constant bank angle) the T&B and TC needles show the same thing.
If you roll out of the turn the same way you roll into it, your timed
turns will be accurate. (This is true using either instrument).
The TC needle will react more to turbulence, but if you react to the
indications smoothly (as I described for straight and level flight)
it will do a good job for you.

I've never seen anybody get that kind of accuracy out of a turn
coordinator.
Bill Daniels

Well I guess you just haven't looked very hard

~Paul