In some respects this would solve a lot of problems. All players would have an equal footing in terms of raiding and PvE technology. There wouldn't be a magic add-on that everyone needs to have to do basic things (Deadly Boss Mods), or one that you should have if you want to be a good player (Recount/Skada). Blizzard would be forced to design these add-ons into the game, or overhaul the game systems to account for their absence. We'd probably see simpler raids and simpler DPS mechanics as a result.
But, that's not a terribly good solution. Ghostcrawler weighs in:
@c0dziraaawh Not really. It's a ton of work to support them, but many if not most players use some. The customization is cool and valuable.- Greg Street (@Ghostcrawler) January 20, 2013
The add-on system WoW has is an economy. Blizzard provides the framework for the utility/value that add-ons provide the community. From there it's up to the community to create the add-ons that will service itself, which then live or die by their popularity and perception of utility in-game. In many ways it's a brilliant system that allows the dedicated players what they want while taking much of the design and implementation out of Blizzard's hands (although as Ghostcrawler notes, the support of the underlying mechanics is quite a task). If Blizzard were to kill add-ons and bring all the "necessary" functionality they provide in-house, then they'd have to dramatically expand their development team, something which is very costly.
At the end of the day, no, Blizzard is never going to kill add-ons. If anything, look for them to expand. A Twitter interface would be amazing.