There's definitely still a place for at least some tackle shops (as long as there are anglers, of course). As others have said, the guarantee of quality fresh bait such as worms and maggots cannot be had on the net, and the ability to see and hold rods and reels is something you'll never manage virtually. I would also say that tackle shops are one of the few remaining high street brick and mortar places where you can still get the odd killer deal that you'll never find online, not even on eBay. Earlier last year, for example, from two separate tackle shops I picked up a new and unused Shimano Purist barbel rod for £80 - cheapest I could find it online was 2nd hand on eBay at £155 - and, again new and unused, a Shimano Alivio medium feeder rod paired with a 2500 baitrunner reel for £45 - the reel was effectively free. I also note that most end tackle items are no cheaper on the net than they are in tackle shops (which could just mean that the tackle shops aren't making any profit on them, or possibly even selling them all as loss leaders), so no massive saving to be had there.
I think the tackle shops that will survive are the ones that have a decent internet presence as well, either their own website (Fishing Republic, Glasgow Angling and the like) or an eBay shop.