Is it safe to use my US iPhone/iPad charger with a simple European plug adapter?
Yes, you can use the simple adapter. If you read the tiny fine print on the plug end you see "110-240V 50-60Hz" which means it will work on most common electrical systems around the world without a transformer.
Yes, it is perfectly safe to use a simple adapter for EU. You do not need additional transformers. When I went in visit to Europe I got one adapter exactly like the one in your post, the black one.