Greece sells you the rental car as romance: open roads, coastal switchbacks, the freedom to find your own beach. On most islands that's a lie. The roads above Oia are one and a half lanes wide with a cliff on one side and a line of rental ATVs driven by people who've never ridden one before. Parking in Fira in August doesn't exist. Lindos has a hairpin descent that tour buses and rental sedans fight over every single afternoon. A car on these islands doesn't buy freedom — it buys a parking problem and a higher chance of an insurance claim.
This list is for the traveler building a Greece trip who doesn't want that fight: someone doing ten to fourteen days, hopping by ferry, walking from the port to the hotel, and using a local bus the three times a week they actually need to go somewhere. It's not for the person chasing a specific undeveloped beach that's only reachable by dirt track, and it's not for someone who actually wants to drive — Crete, the Peloponnese, and parts of Naxos reward a car in ways these four islands don't.
Santorini, Hydra, Paros, and Rhodes solve the car problem four different ways, which is the point. Santorini has a cable car, a donkey path, and buses that run the caldera-rim towns constantly, if slowly. Hydra has solved it by banning cars outright — mules and water taxis only, since forever. Paros has a real bus network connecting Parikia and Naoussa on a schedule you can set a watch to. Rhodes has a walled Old Town built for feet, centuries before anyone needed to park, plus buses out to Lindos and the beaches. Different mechanisms, same outcome: you never need keys.