From what I've heard Mike Okuda say, money isn't the issue; they
want to be as faithful as possible to the original episodes. If anything, I'd imagine that tracking down, remastering, and recompositing all the original bits of film that the FX shots were made from would be longer, harder, more involved work than creating all-CGI reconstructions, so I'm not sure any money is being saved.
As for that YouTube video, I don't see any material difference between the original shot choreography and this version.