Unfortunately public transport options are meagre. The only feasible option is the KTEL coach service which requires a trip from AIA to Kifisos bus terminal. I'm sure that you aware that this is not a pleasant ride through the city; time-consuming and prone to delays. And until the bus terminal moves to their new location I personally would suggest to try to avoid it as the place is quite...lets call it 'rough'. Having travelled to this part of the country many many times I can tell you that from a comfort perspective the flight really is a lot better and faster. Especially when booked in connection to an international flight (Meaning a short transfer at ATH).

The flight does not operate during winter in any case; so its clear that the target audience is tourists. Which of course makes sense, KLX being close to costa navarino and mani - this is a very popular area with tourists (And not unwarranted, Mani - especially the Laconia part - is really worth visiting imho).

Locals originating in ATH would probably indeed be much better off driving or taking the KTEL service. I don't think thats the target audience for Aegean though.

Edit: And to add, the KLX-SKG service is - as far as I am aware - a PSO route. Meaning that this is government sponsored and not relying on actual demand.