Routing protocols can run only on primary address (at least on Cisco routers), however they can advertise other addresses. RIP and EIGRP internal routes will always use neighbor as next-hop of advertised prefix, OSPF is slightly more complex but at the end next-hop will be either ASBR (and then recoursively looked up) or one of directly attached neighbors. The only protocol that can modify next-hop of advertised prefix is BGP and then only to...IP from which iBGP session originated (by applying next-hop self).

Since there is no way to source routing protocol packets from anything but primary address of an interface, and HSRP virtual address is not primary address, then it's clear why HSRP cannot be advertised as next-hop directly.

One possible trick is to have some dummy route pointing to HSRP address, then it can be redistributed either into OSPF NSSA area (if OSPF is running and not passive on HSRP facing interface) or into BGP (if it's eBGP with neighbor on the same subnet as HSRP or it's iBGP without setting 'next-hop-self'). But hard to see what's use of HSRP address beyond local subnet.