I don't think state machines are anti-modular, but I've seen situations where a cartesian product of several state machines was modeled as one big state machine

I don't think state machines are anti-modular, but I've seen situations where a cartesian product of several state machines was modeled as one big state machine, rather than as several largely independent state machines running in parallel. The one big state machine ends up as an anti-modular un-abstracted hard to read mess. Imagine writing a state machine to handle TCP/IP connection establishment, and a state machine to handle parsing HTTP headers, and a state machine for the different things your web app can be doing. If you combine them all into one big state machine, you're going to have a huge mess. If you can write separate state-driven modules for each, interacting with each other at well-defined interfaces, you'll be much better off. In other words, state machines, like most tools, can be abused. Don't do that!