well you could say the same about "smartphones" and alot of devices in this world, if you are going to buy a Smartphone/tablet (even windows 8 computers with a Microsoft account attached to it), you wont be able to use it more than a dumbphone without internet, but people dont seem to complain about it. you cant buy or download games, you cant check your email, you cant use skype or whatsapp, or YouTube, or use turn by turn navigation, and well... you cant do almost anything, the OS expect you to do.
Also you dont even know what kind of DRM publishers are going to put in PS4, so you dont know today if not having internet would let you play 3rd party games there. since a game could ask you to be always online, or put a serial and authenticate it, so no internet, no games.
But I find it dumb to think you would buy a modern console with a vision Microsoft is having with Xbox One, spend $400-500 and don't have money to put internet on it.
I mean.. have you seen all the internet features xbox one has? or the cloud vision Microsoft wants in xbox one? better get the son or daughter or whatever example you want to say, a book and give them something more educative, than an expensive console that wouldn't even have internet access.