Digital distribution is the future for a very simple reason: it is convenient.
You can argue it's not instant, but what if your nearest game store is 15+ miles away? What if your nearest game store doesn't have the game you want? What if you don't want to wait most of a week for your game to show up in the mail because you chose the lower price in exchange for slower shipping? What if you don't have convenient transportation? What if the store is far enough that the price of gas spent makes your game cost enough that it's no longer worth it?
Digital distribution removes every single one of these roadblocks. You can find the game you want at the retail price you'd be paying anyways, and add it to your console library in a few clicks. Then you may spend four or five hours downloading the title, but you saved money by not physically going to the store and you save time by not waiting on shipping. The only downside is that digital prices don't always match the decline in physical prices, and thus, you end up with a Nintendo situation where their eshop current gen releases will always stay the price the physical item launched at. Steam is probably the only platform that successfully navigates around this issue, and I can only hope that the big three console developers pick up on that and follow a similar pricing model. Discounts on games only really happening during sales on consoles is certainly inconvenient.
The other big issue with digital distribution is that sometimes, like with the Vita, games may become a store exclusive, thus, they are never available for digital purchase, and you are completely confined to physical copies that weren't plentiful to begin with and quickly go up in price as the low stock declines. This one doesn't happen often at least, but as physical game stores continue to decline, I could see situations like that becoming more common so that places like Gamestop can generate more business for themselves.
All in all, digital distribution on consoles is still highly imperfect. PSN is probably the closest we've gotten to something like Steam, and PSN still has a long way to go before it is a truly effective digital distribution platform.