@Ixidane Most of the players doing LFR just didn't raid at all before. They were never really eligible for recruitment.
— Greg Street (@Ghostcrawler) June 6, 2013
First of all, the above tweet by Ghostcrawler indicates that Raid Finder players and normal mode raiders tend to be two different sets of people. There's certainly some degree of overlap, but by and large, players running Raid Finder are brand new raiders as opposed to former raiders. This calls the entire initial assertion into question, and considering Blizzard has access to far more data on the matter than the playerbase does, I'm willing to believe they know what they're talking about.
So, if normal mode raiders aren't switching over to using Raid Finder as the sole fulfillment of their raiding desires, what's happening to them? As odd as it may sound, I think the answer lies within a nearly year-old article posted on GamesIndustry International just after the launch of Mists of Pandaria - Blizzard's success isn't magic; just hard work and open minds. The article isn't terribly long, and I highly suggest reading it in its entirety, but the key point is essentially that Blizzard has always aimed for accessibility, and as World of Warcraft becomes increasingly accessible the vocal hardcore players become flummoxed over the fact that Blizzard isn't treating them like the influential "whales" that conventional gaming wisdom tells them that they are, and so they begin to complain about this process. The Raid Finder and other systems that are perceived as "catering to the casuals" become the scapegoat for hardcore players' ire, and I think this following tweet shows exactly that happening, as well as posits a more likely explanation for where these normal mode raiders are disappearing to:
@IshayuG The fact is, WoW always lost lots of players. In the past, we tended to get as many or more new ones as we lost. Lately, less.
— Greg Street (@Ghostcrawler) June 8, 2013
In other words, players aren't abandoning normal mode raiding in favor of Raid Finder, but rather the available pool of normal mode raiders is drying up as the overall playerbase contracts. However, even if World of Warcraft's subscriber base continues to erode, there are still upcoming features that will likely serve to boost normal mode raid participation. Flex Raids will allow Raid Finder players to get a taste of more standardized raiding, and hopefully convince them to move up to normal modes once bitten with the formal raiding bug; and Virtual Realms will consolidate player populations, allowing raid groups greater access to players who are interested and available for raiding, but unwilling or unable to transfer realms to do so.
Hope is not lost. Keep calm and raid on.