Fakebooks also improve classical playing. Learning how to read a lead sheet format forces a musician to internalize core music theory principles. A common classical music pitfall is relying too much on shallow rote learning, black dot = push down key without the substance of musical grammar & vocabulary.

I often see classical music as a lead sheet with the written notes being the composer’s suggested arrangement technique. It takes some time to see the collections of dots (notes) as higher level pattern like chord symbols but it all leads to the same place!

[edit] your playing becomes less fake by learning how to fake from a fakebook!