Here's an analogy:

Take a vertical pipe in CAESAR. Anchor at the bottom, free at the top. Apply a horizontal displacement at the top node of L. Run and calculate the model. You have a force and a displacement, therefore, you have a stiffness of F/L.

Now, if you double that displacement, you're going to find a different force for that displacement, and a new stiffness value.

If you repeat this exercise, you can plot F/L, and you'll get a curve. Should be what matches classic beam theory.

The same applies to these expansion joints (as well as spring cans etc). The issue is, we approximate this stiffness through linearization and accept a set amount of error when we do so. For spring cans, we limit our load range to 25%.

While I can't speak for expansion joint manufacturers, it would seem to be a daunting task to provide accurate stiffnesses over a range of values, when you have so many ranges to work from.

For springs, you have 1-directional displacement and stiffness only. For expansion joints, you have 6 axis displacement/rotation, plus pressure, plus any other special considerations for any given expansion joint. Did I mention these 7 dimensions also interact with each other?

Even their outdated values are going to be better than a rule of thumb, which is made in the absence of specific data.