> Then couldn't I just follow the same patterns in a modular monolith (eg: avoid shared state, make sure errors are handled properly, etc) and get the bulk of the benefits, without having to introduce network related problems into the mix?
Sure. Microservice architecture is a set of design patterns and a discipline for knowing how to structure your applications.
Many, including myself, would argue that by leveraging patterns such as separate processes as a focal point for the architecture leads to patterns that are harder to break out of and abuse, but of course anyone can do anything.
Error handling is the easiest one. With any 'service oriented' approach, where processes are separated, you can't share mutable state without setting up another service entirely (ex: a database). Microservices encourage message passing and RPC-like communication instead, and it's much easier to fall into the pit of success.
Could you do this with functions? Sure - you can just have your monolith move things to other processes on the same box. Not sure how you'd get there without a process abstraction, ultimately, but you could push things quite far with immutability, purity, and perhaps isolated heaps.