Why does it take 10 minutes to reboot the modem?

Some modems take longer than others. Some of the arris modems take exceptionally long, as instead of locking in channels by groups of 8 like some, they do so, a single channel at a time, to ensure the fastest possible connection. That's a hold over from the old Motorola Surfboard line. Slower boot, faster throughput. I have an old DG2460, takes 6-8 minutes to boot, but I can tell you, it's extremely fast, even if it is over 7 years old.