Cable modems are powered up and online 99.9% of the time, little to no productivity is being lost here. If it makes the engineers' lives easier, up to 5 seconds would be totally reasonable, in my opinion.
If you want to talk about human productivity being pointlessly wasted while waiting for things to load, let's start with modern web apps.
That or just simply the sheer percentage of Comcast downtime, or the percentage of time their stupid DHCP servers give me only an IPv6 and not an IPv4 address, and their support just gives me the "Is the power button in the on position" type BS and the support person doesn't seem to even know what DHCP is.
Fun fact: The USB logo should be facing you when the cable is inserted in the correct orientation. Ever since learning that, the magic "turn it around three times" has stopped happening to me.
If you want to talk about human productivity being pointlessly wasted while waiting for things to load, let's start with modern web apps.