This is the biggest reason why the PS4 is so successful, though I don't think you're quite right about MS not targeting high end graphics as the reason.
Nintendo didn't market the Wii U at all and failed to explain to consumers how the console is different from the Wii. Nintendo also had abysmal first party support in the firs year or so of the Wii U's life and didn't really pick up until 2014, and by then it was too late. I've had my Wii U since October 2014 and I have friends who still ask what is that small black box connected to my TV. They don't even know the Wii U exists.
Microsoft left a huge bad taste in consumers mouth with the reveal of the Xbox One. It's the fact that they initially marketed the Xbox One as an entertainment center first and a game console second that pushed so many people away from the Xbox One. Hell, I was one of them and I adored my Xbox 360. That shit storm of initial marketing along with the fact that they didn't announce a new Halo or Gears of War yet only hurt the Xbox One's image. Like the Wii U, the general populace is still horrendously misinformed. I have friends who, until I had to correct them, still thought that you can't play used games on the Xbox One and that you have to be always online.
I'm not a fanboy by any means but the whole "PS4 has no games" is very understandable to me. PS4 has yet to have a God of War, Gran Turismo, New Uncharted, Ratchet & Clank, Resistance or Jak & Daxter game. Granted some of those are coming out but Nintendo has already pushed out a ton of first party titles and Microsoft has had 3 Forza titles, Halo 5, a Gears of War Remaster, a collection of Rare Games, Killer Instinct, Titan Fall, & Sunset Overdrive. The core of Playstation 4's exclusives has either not come out yet or quickly forgetten (Knack, Killzone Shadow Fall). There are outliers like Bloodborne and Until Dawn but the most hyped PS4 games are not out yet (Uncharted 4, Street Fighter V, The Last Gaurdian, Horizon Zero Dawn, Persona 5) and some won't be out for a very long time like Shenmue 3 or FF VII Remake.