What's the practicality of landing on a deserted island to save someone?

The most likely scenario would be a ship is sent to the location and the ship stays off shore where the water is deep enough and then launches either a helicopter or small rescue boat that can go onto the island to rescue the person.

It is possible to land a small aircraft on a sandy beach if there's a stretch that long enough and flat enough, but they would probably not take the risks

Call a rescue team that's equipped with the appropriate transport, ie an amphibious plane or a helicopter or boats. 

You can land on a flat Sandy beach if it’s big enough. On the Island of Barra in the Scottish Hebrides, scheduled flights use the beach as a runway. Of course the timetable has to fit in with the tide.

A pilot would want to make sure there was a safe way to take off before landing! Odds are that the location would be sent out over the radio and forwarded to the Coast Guard or USN (and any other ships in the area) to effect a rescue.

If there is someone on a "deserted island", it's no longer deserted. 

Dear; when I still had my plane I landed on the road behind my house and taxied into my yard. I no longer own one - got too expensive.

My neighbor lands in a grass field near his house and he's flying a Citation. When he flies bushplane "UP NORTH" he regularly lands on the highway.

And down on the prairies it's not uncommon to see spray aircraft parked on grid roads to reload.

In the USA I've flown with groups who go to remote locations and land wherever they can just because they can. 

None of us ever asked permission to do so unless it was private land..

How about a helicopter or a seaplane?  A boat would do the trick as well...

None of the above requires any sort of runway.

Helicopter?                                  

Not a problem, hardly an inconvenience.

Just call it out to a nearby rescue service, Coast Guard, or Navy, maybe even a merchant vessel, and be on your way.

FAA permission is not needed to land off airport.  If there was a big enough field or hard packed sandy beach to land on, no problem.