Periodic reboots are actually a PCI requirement for payment terminals heh, basically every point of sale on the market reboots every 24h.
Seems like a good defence in depth strategy. These days most systems have a pretty good boot chain security, so after a reboot you know the system is in a valid state and any potential malicious changes have been flushed out.
But wait for security cargo-culters call it "security by obscurity"
All that private key nonsense falls in this bucket as well. What else is a private key than an attempt to guard your system behind a thin veil of "an obscure number I know and you don't"? Classic security by obscurity.