> competent enough to recognize an attacked modem, and repair or replace it on demand

The cable modems I've interacted with all seem to be immutable infrastructure: their state consists of 1. a signed firmware image; 2. a DOCSIS initialization packet received upon network registration (essentially equivalent to a cellular "carrier profile"); 3. a set of saved preferences; and 4. some volatile working state, like ARP tables or WPA encryption-stream key state.

#4 gets trashed on reboot; #3 shouldn't be large enough (or executable) in a way where programs can run from it; #2 gets overwritten every time the network reconnects; and so the only place to put a persistent malware vector should be #1. And #1 can only be written to using signed code (sort of like Intel CPU microcode.)

So what's the problem that can't be solved by rebooting the modem?

Not my experience. My parents are stuck with Comcast due to their monopoly and even they bend over backwards to fix my parents recent issues (hardware failure). Sure it took a couple weeks, but it a couple weeks of troubleshooting, testing, a couple visits, some hardware replacements. People expect these repair installers to be miracle workers, but sometimes an intermittent fault takes time.