It seems to be out of fashion because black does far better in the Capablanca variation. Negi's book pretty much closed the case; all the important games had already been played until about 2013.
The critical continuation is the following line:
leading to two critical positions:
In this position the assessment seems to be a slight advantage for white without any serious counterplay for black. Black did not win a single game in this variation in the last two years or so. I will not go into further detail; Negi's analysis seems convincing.
The other position is this one:
Here in the critical line white delays castling with Ne5 and Bd2 and usually even f4, waiting for black to show his cards. White will castle the other way and hack open the black king. This is pretty much what Negi recommends for white. White has a huge plus score with almost no losses.
I spent some IDeA time on a move order against this for black, delaying ... Qc7 by ... b6 und ...Bb7 first and gaining the option to play ... Bc7 if white sticks to his scheme. White still gets his usual slight edge I suspect, but it seems to me that black is holding his own here. I also found some other interesting practical ideas for black against this move order, so at least I am not scared to play this OTB with black.
Probably absolutely not because of this but rather for practical reasons, white players still use to opt for the old main line defined by castling long first and not necessarily playing Ne5. White still scores above 60% there, which is not bad at all for an easy-to-play second best line. It is, however, the way people played before Negi's book and nothing black players used to worry about. As far as I know there is no brand new theory on this; this is just a very classical position which has been played a lot.
So the variation starting with 10. ... Nf6 is the way I would go for black if you want to play the Karpov variation.