flying into Athens, Santorini, or Mykonos?

Is it possible to ferry over in the morning and catch an afternoon flight?

"Possible" - maybe, but I suspect the majority ( by a clear margin) would advise to be in Athens the night before a flight

Athens Airport is quite crowded in season. Ferries have been known to be canceled in turbulent weather.
Flights can get delayed or even canceled. So, it is best to be prepared and stay in the city the night before you have any international flight out of that city.

Islands like Naxos, Paros etc are not less touristy or low key unless you are travelling in low season. They are packed to the rafters in high season. Airports are very busy, particularly international ones like Athens, Santorini and Mykonos. Ferries can get cancelled or run late in windy weather and due to other causes (strikes, mechanical failures) - you will have to keep an eye on the weather forecast and news and react quickly (if you can, it may be too late before you become aware of a problem).

As others have eluded it is not how crowded the airports are but where you are the day of your departure. Nearly every " wise" traveler to Greece always recommends being in Athens ( or close by on the mainland) the day of your departure. Even a connecting flight that morning from an island is risky. Weather, delays, strikes, can derail your trip home very quickly. Best to give yourself a night in Athens before you leave.,

All the Cyclades islands are more or less touristy. If Santorini and Mykonos are ranked in 2 first place, Paros and Naxos are just after tied for the 3rd place. So if you are looking for an island that is less touristy, with Naxos and Paros you are on the wrong track.

In the Cyclades islands if you are looking for a less touristy island, look for Tinos, Sikinos, Kythnos, Folegandros, Kimolos or Serifos, and also Amorgos that you mentioned

Find them here:

https://www.visitgreece.gr/islands/cyclades/

You'll have the same whitewashed houses and the same beaches, but with fewer crowds and cheaper prices.

Over the years I have seen quite a few tourists panicked because their ferry was canceled and they were stuck on their island while their flight home took off from Athens.
I myself experienced this kind of situation during my first trips to Greece, before the era of the Internet and cell phones.

So it’s up to you to see if you want to take the risk. Personally I don't take it anymore.

Thanks for the input! So, it sounds like we should definitely plan to travel to the place we're flying out of the day before, that's really helpful. Can anyone speak to the ease of getting from port to airport, and through airport, for Athens vs Santorini vs Mykonos? There's not a meaningful price difference, so it will come down to which place is easiest to get to and through! Thanks.

In all islands with an airport you can easily go from the port to the airport either by taxi or by bus.
This is not what matters most in organizing an island hopping trip. First, worry about which islands you are going to, which ones have an airport, and which ferry trips are to be planned.

Depending on your dates, check the ferry schedule on ferryhopper.

https://www.ferryhopper.com/en/#/

Our approach is to plan our flights in and out, then pick the islands that we'll visit in between. This lets us snag lower plane tickets now, and have a bit more time to make decisions about where to go (since this is a last minute trip!), knowing that we'll start in X place and end in Y.

I just read on some older posts (8+ years) that the Santorini airport is fine to fly into, but chaos to fly out of. Does this jive with anyone's recent experience?

If your approach is to determine your trips based on cost, you will also have to look at the prices of ferry tickets.

For example a Santorini→Amorgos ferry can cost between €11 and €78 per passenger depending on the type of ferry and the day.

A Mykonos → Amorgos costs around €90/passenger, but if after Amorgos you go to Naxos the ferry price varies from €11 to €70/passenger

So what's the point of choosing an airport with flights 50€ cheaper if you have to pay 120€ more in ferry tickets?

So looking only at the cost of flight tickets is pointless if you don't also look at the cost of ferry tickets, because all the main differences in price, logistics, and possible chaos will depend 90% not on your arrival and departure airports but on the islands where you can go depending on the available ferry connections and their schedules.