As has already been noted, the EJ&E and IHB are hardly "small railroads." Indeed, they are officially Class 2 Terminal Lines (if I remember the terminology correctly). Terminal roads don't get a cut of the line haul, but they do charge their connections a "switching fee" which can be substantial.
I don't think Class 2s had to contribute cars to the national fleet in proportion to their revenue like Class 1s did, but many of them had significant originating traffic and it behooved them to own cars to protect the needs of their shippers. This would explain the EJ&E's and IHB large fleets. I also got the impression the NYC used the IHB as a way to make sure their steel-service empties got sent back to the Chicago end of the system rather than simply being dropped off at the nearest NYC interchange. which you could do with a car marked "NYC".
Class 3 lines, what are tradiationally thought of as shortlines, do not have to contribute cars to the national pool, and their connecting Class 1s have to supply cars for interchange traffic. Shortlines only had to own enough cars to meet their own captive movements, like LCL service, or in the case of the Yosemite Valley, limestone service between a quarry and an on-line Portland cement plant. Only shortlines that had a lot of originating traffic, or needed special cars to handle their interchange traffic, owned cars that freely roamed the national rail network. One example that comes to mind is Buffalo Creek, which served a bunch of flour mills. I gather the BCK didn't have a lot of interchangable cars until after WW2, however.
The other big exceptions to this rule were the switching lines owned by steel mills like USSteel and Bethlehem. They often had a bunch of gons to protect their originating finished steel products traffic.
It wasn't until the Incentive Per Diem craze of the '70s that many "normal" shortlines leased their own boxcars, and that was driven by other considerations, not originating traffic. Besides, that's well after the period covered by this list.
Scott C