Can the PS4 renew the lack of home console gaming in Japan?

[Mummelmann]

No, pretty sure it can't. It appears to be more or less exactly on the same path as the PS3, which didn't cause tidal waves in Japan.
The main problem is that global developer culture has moved farther and farther towards a Western-centric position and there just isn't that much focus on traditional Japanese gaming any more.
Even games and franchises that had that unmistakeable Japanese tinge to them have changed a lot (Resident Evil would be a prime example) and moved a lot more towards the Western and more action oriented segment of gaming.
Some are also being relatively successfull with this recipe, Demon's Souls is a good pick for that; it has a Japanese sort of structure but a Western look and feel to it and a lot of the gameplay elements have been taken closer to the ground and less over-the-top, the combat is sombre and to the point, unlike the more traditional Japanese recipe with colors flashing over the screen, crazy air-juggling combos and 50 hit super special ultra kill attacks.

Whether or not this is a good thing overall is not for me to say, personally I'm not opposed to either approach in principle but I think it's a shame if one takes over entirely, leaving the market less diverse.
One thing seems certain though; all this is causing Japan as a gaming market to lose interest home consoles, especially with a Western centric philosophy, the Xbox brand is dead over there and the PS3 and PS4 is and are turning into a slightly more Japanese Xbox, and the Xbox is becoming a slightly more American Playstation, they're meeting in the middle and essentially fighting over the same customer.

Due to these rather minute differences though, which are more in perception that actual offering and direction, the Playstation will have the upper hand in Japan and the Xbox will have the upper hand in America.