They are relatively insensitive to initial conditions . In terms of predictability, this is very good behavior. Since Newton, it has been assumed that real-world dynamical systems are insensitive to initial conditions. If I break in a game of billiards, the balls will move in a specific manner. This insensitivity to initial conditions is very important.
Uncertainty of measurement comes into play here.
There is a principle that states that there will always be an uncertainty in any measurement, no matter how precisely we can measure. Say we measure out one inch. Say we can measure our inch to ten decimal places. We have a measurement of 1.0000000000 inch. If a system is linear, it really does not matter that we cannot have exact measurements.