Why should IGP advertisements be disabled on an access link where a host is attached?

While hosts typically do not run routing protocols, the concern is not the host's capability - it is the risk that any device on that link, including a rogue one, could inject bad routes into the router.

A host or rogue device connected to an access link could send crafted routing protocol packets (OSPF Hellos, RIP updates, EIGRP packets) that introduce false routes into the IGP topology. Using a passive interface or similar mechanism suppresses IGP sending and receiving on that link, blocking route injection and protecting routing table integrity.

Reducing router overhead is a minor side effect of disabling IGP on access links, not the primary security motivation for the practice.

Whether edge hosts are statically routed is a host configuration detail that is irrelevant to why the router should not advertise or accept IGP messages on the access link.