why can I only ping (from Network A) Router1's interface on Network B, but I cannot ping Router2's interface on Network B?
Because R2 does not know how to get to NetA. This is the purpose of routing protocols: to allow routers to tell each other about networks they can reach.
If you don't want to run a routing protocol, add a static route on R2:
ip route 192.168.10.0 255.255.255.0 192.168.30.1