It's not really CL's fault. The PACER/ECF sites for the various Circuit Courts are themselves weirdly fucked in different ways, and often really finicky to query. Also the client doesn't upload. I'm not sure whether they've deliberately broken it or just haven't implemented it.
It's somewhat frustrating as these are the cases that actually make law.
Lexis and Westlaw do better at these dockets than the federal appellate courts (as if I am paying their rates for this).
On the good side most of these sites (maybe all I am not going to check) often have a page for recent briefs so if that's all you're interested in, you can get them for free. Another good aspect is they usually have an appendix with submissions from both parties. This means you can get the entire relevant trial court document in one document (or several if it is multi-volume), but the prices max out at I think $3 a document, so you can get the trial court record while only purchasing a couple documents.