As I get older and my handicap gets higher I am pleased to hit the green on any par 3. However, I am always conscious of where NOT to go. All departments of my game are lacking, so I would never deliberately aim to miss a green, because I could not guarantee to get up and down from a difficult bunker (2nd green, front right bunker at R Dornoch comes to mind) or, possibly harder, a grassy swale. I do, on occasion, deliberately play short of a narrow entrance to the green if there is the possibility of putting from there.
I do have a good memory for golf holes and I remember a lot of short holes with affection. Sometimes it is because of the setting (RCD 4th) added to the difficulty posed by so many bunkers. You don't easily forget the 4th at RW Norfolk with its sleepered defences. You don't forget the 7th at Hunstanton across a valley and a 'must carry' cross bunker. You don't forget the excitement of the back-to-back par 3s around the turn at Brancepeth Castle, although I doubt if could make the carry on either. You never forget any of the par 3s at Rye. And so on? And, of course, these holes change daily with the vagaries of the wind. Do you forget the short holes at Painswick? Surely among the most memorable of all, although they may not be great holes.
And, as Duncan says, holes you know well you may well play more intelligently, and what is the correct strategy for one player may be wrong for another. At Fairhaven the other day my elder son was hitting the tee shot on short holes at the flag. His strategy worked. I aimed at the greenside bunker on whichever side the wind was coming from. Largely that worked for me as my shot has far less energy. My wife, who was often hitting 3-wood into the short holes was looking to run the ball onto the green, her trajectory much lower and below the wind.
Designers are designing for all these categories of golfers and a short hole that offers options will please more punters than some all-or-nothing do-or-die confection. There are, after all, even bail out options on 16 at CPC or 11 on TOC. I am no longer too proud to accept that option.