That is not always the case.
Some networks are (way) more complicated than that.
FYI, the best IP-routing protocol is IS-IS !!
You left that out of your list, so I thought I should mention it.

(Yes, IS-IS used in all the big ISP- and telco-networks. Enterprise networks more often run OSPF. But IS-IS is technoly-wise the better protocol (imho). I prefer IS-IS over OSPF. By far).
Whether it is necessary to run a routing protocol depends on the topology of the network. The important thing to understand is: routers and hosts know only about directly connected networks (and their ip-prefixes). If a host (host = PC, laptop, server, any device that is not a router) needs to talk to device that it is not directly connected to, it will send the packets to its default-gateway. But for routers it doesn't work that way. They don't have a default-gateway, they need to have routes in their routing table. First they put the prefixes of their directly connected interfaces in their routing table. But if there are more prefixes, of networks they are not directly connected to, they need to learn about those prefixes. Where they are.
network1 --- router --- network2
In this topology, you don't need a routing protocol. Because the router knows about both network1 and network2.
network1 --- router A --- network2 --- router B --- network3.
In this topology you do need a routing protocol. Because router A does not know where network3 is. And router B does not know where network1 is. The routers need to tell each other of network1 and network2. And they do that via a routing protocol.
Of course some human can manually configure static routes. If you do that, you don't need a routing protocol. But in bigger networks, that is not practical. And therefor you do need a routing protocol. Less configuration. And less opportunities to make mistakes.
Yep.
As soon as you have more than 1 network and more than 1 router, you need a routing protocol.