Can $L=SL$ be shown with the replacement product instead of the zig-zag product?
There is a paper already in 2005 that describes how to do this...
See https://people.seas.harvard.edu/~salil/research/derand_squaring-abs.html

I cannot say why people use zig-zag instead, other than perhaps they found the original reference readable enough that they did not need to look at secondary literature. At least for teaching purposes it seems the replacement product is simpler, as the above link shows.