That's actually a good point in the sense that when ICQ was popular most people didn't have a digital camera in their pocket with instant upload capability so sending a dick pic would have been way more trouble.

Maybe the fact that pretty much everyone has a digital camera in their pocket now means the world has changed into a world where ICQ as the OP described it just can't exist anymore

Definitely, the context changes and brings new challenges... but I don't think that's unsolvable. I can think of low-tech solutions (allowing only text, not pictures, until the other person explicitly allows pictures) and high-tech solutions (dick recognition via neural networks).