I guess it would depend on your Topology and network requirements. You would see that GRE Tunnels are used in environments where multicast is supported as well. So it's more of knowing what your network demands,
For eg: GRE Tunnels etc are used in OSPf environments where you want to influence routing between areas etc or preferring inter area routes over intra area etc. just an example.or to advertise routes without actually redistributing them into another routing protocol etc. lot of scenarios where you use GRE.
My question is, if the environment didn't support multicast but you were using static EIGRP neighbors, or even BGP would there be any need for the GRE tunnels in this instance?
Yes and No, consider a NBMA network where you have eigrp neighbors unicast rather than multicast In this instance you might not need GRE Tunnel. But if you had a network where you had static routes all over the place, you can still use GRE Tunnels. Lets says you have R1-R2-R3 . all know each other via static routes and no multicast routing protocol used. If you need network behind R1 to talk to network behind R3 without R2 knowing it then you can createa GRE Tunnel.
HTH
Kishore
