I don't think you can permanently delete them but you can hide an app by sliding left on iOS.
Oh when could you do this directly on one's phone? Only knew the iTunes hiding option.
My bad, I just tried it on my iPhone. Apparently, it only works on the iPad.
It works on the iPhone too (that is, swiping to hide with Family Sharing enabled). Tested on an iPhone 5 and 6.
It's easy to set up Family Sharing, too, and you don't need to actually share with anyone else. I only set it up so that I could hide old apps from my phone.