CTE for Steels
This is a compilation of the CTE's of a hundred or so different steels.
As you can see the normal gage block steel, at 11.5 ppm/°C is somewhat on the low end of the distribution.
The question here is, if you are given a part and told it is steel, what do you choose at the CTE. If "steel" is all you know, the best bet would be about 14 ppm/°C and the uncertainty would be about ± 3 ppm/°C.
For high accuracy parts this would be a serious drawback. Of course, you would have to get in touch with someone who could tell you which type of steel you were measuring. That might help, although not as much as you might think.