PS4 does have the support of casuals, and we have data points showing owners who didn't previously own a PS3 or 360, and instead owned a Wii. Then we have a segment that didn't own any console in the previous generation. The distinction between casual and core gamers is based solely on their engagement level. Franchises like Call of Duty, Grand Theft Auto, and Fifa, tend to appeal to casuals too, which is part of why they're so successful. Casuals isn't used as a blanket term to group in different demographics and audiences in reality like it is on GAF. You have different segments that you have to appeal to in different ways.
SCE's modus operandi is to pitch the PS4 as a mass entertainment device. That isn't any different than it has been since the PS2 era. The current demographic split on the PS4 is better balanced than it was on the PS1 or the PS3 from consumer data, so we're already aware that it's positioned quite well in respect to what's been accomplished in the past. The plan isn't to focus on just core gamers or casuals at different points in the life cycle, but instead to increase engagement levels of core gamers, while continuing to court casual gamers, and convincing them to buy in to the platform. There's evidence of that already slowly happening, which is why PS4 is so successful, but the larger problem is there are many price conscious consumers who you can't really target until the price becomes further reduced. That's more of a long-term strategy however, and will take effect from 2017 onwards. Beyond that, the future of PS4 is much more secure than the PS3 simply because of inroads being made in other markets, and the more flexibility PS4 will afford at the end of the generation due to various factors.
Of course, none of this really helps with the real issue of it having no games, but what can you do? You win some, you lose some. That's life.