The title isn't quite correct. He explains /bin vs. /usr/bin, but not /bin vs. /sbin.
My understanding for the latter is that /bin is "normal stuff", while /sbin is system maintenance. But, hey, maybe that split is actually there for obsolete historical reasons, too. Does anyone know?
And the reason for splitting them is so that normal users don't have the super-user programs in their $PATH, since they would be useless there. Of course, this is arguably obsolete now since the advent of sudo, policykit, and so on.
Conventional (that is, without capabilities) traceroute and ping were setuid root because it there was no provision for emitting ICMP packets in the network APIs and only root could assemble raw packets.
The particular way traceroute runs is implementation-defined. Some use ICMP echo request packets (ping), which you have to be root to send on most Unices. Most of them, however, use UDP packets instead.
My understanding for the latter is that /bin is "normal stuff", while /sbin is system maintenance. But, hey, maybe that split is actually there for obsolete historical reasons, too. Does anyone know?