My problems with them being that they cram together pieces of information that could be considered separatedly.
For instance you could write a FSM that transitions from "paid" to "delivered"... or you could have two columns, paid_at and delivered_at, and consider those two columns orthogonal.
As I see it, it scales better for humans - it's easier for us to consider 10 or 20 things separately than as part of an intrincate, bespoke rule system.
You can still have some simple validation rules e.g. "delivered_at can't be set if paid_at hasn't been set". Which probably, if you squint is like a FSM in some mathematical sense, but in practice much complexity is avoided.