The Fried Liver Attack

Some ways that Black can be less cooperative:
5...Na5 instead of 5...Nxd5.
3...Bc5 instead of 3...Nf6.

But what if black plays this variation?
There are two powerful options for white: 6. d4! (Lolli Variation) and 6. Nxf7?! (Fegatello Line)
Nxf7, the knight sacrifice, is harder for beginners to defend. Opponents of this move say that, if black plays carefully and correctly, they can defend the knight and repair the king's position in the center. Believers in this sacrifice say that the king in the center, coupled with the fact it's attached to defending the attacked knight, is enough compensation for the two pawns down in material that white is.
As I haven't experimented with the idea 6. d4!, I cannot speak for the theory behind this move. My FCO (Fundamental Chess Openings, by Paul van der Sterren) says this is better for white than Nxf7, to quote: "The preliminary move d4! is even stronger. If 6... Nxd4? 7.c3! and black simply loses a piece, while 6... exd4 7. O-O gives white a terrific attack along the e-file." (Page 308).
What is with this obsessive need for trying to get the fried liver attack on the board. It's fried liver here, fried liver there. I mean the attack is not even that appealing estethicaly, and on top of that 99% of players are not gonna fall for that anyway. It's like a chess kindergarden kind of trap.
There are two powerful options for white: 6. d4! (Lolli Variation) and 6. Nxf7?! (Fegatello Line) ... My FCO (Fundamental Chess Openings, by Paul van der Sterren) says [6 d4] is better for white than Nxf7, to quote: "The preliminary move d4! is even stronger. If 6... Nxd4? 7.c3! and black simply loses a piece, while 6... exd4 7. O-O gives white a terrific attack along the e-file." (Page 308).
If I remember correctly, FCO was a 2009 book. Apparently, within about a half-a-decade, there was some new thinking on the matter:
"... in a period of a few years, century-old theory had reversed. Instead of the popular Fried Liver [(6.Nxf7)] being considered the inferior response to 5...Nxd5?! and the Lolli 6.d4 the one that refuted it, the roles changed! The Fried Liver was placed on the pedestal and the Lolli relegated to the notes section. …" - NM Dan Heisman (2014)
https://www.chess.com/article/view/how-do-i-get-that-1800-into-a-fried-liver
Perhaps it is of interest to note this game:
https://www.chessgames.com/perl/chessgame?gid=1765926
I don’t know what thinking there has been since then.
... even if white opts for it after being allowed, black has an edge with correct play.
Do you have in mind a specific edge-obtaining improvement for Black in this game?
https://www.chessgames.com/perl/chessgame?gid=1765926