It doesn't seem to me that a ship takes all that much strain through the course of flight & combat (outside of Ion Weaponry). What are examples of a ship taking Strain?

Umm... then I think you might have missed some things. The biggest example is that if the pilot wants to do two things with the ship in a single round, the ship takes 2 system strain, just like a character taking two maneuvers in one round. That by itself is the main reason for the ship in our campaign slowing down.

Most Critical Hits inflict system strain as well; and any Threat on Piloting checks can inflict system strain on a ship, just like Threat on personal-scale checks. Additionally, there are a couple maneuvers that inflict system strain, such as Punch It!, which inflicts system strain equal to the change in ship speed.

Run the numbers and look at all options. Taking a second pilot only maneuver, threat, lots of crit results...

And you can't recover system strain with advantage.

When talking small arms vs vehicles crit results that produce system strain are one of the primary ways of defeating the vehicle.