From what I've been told there's a lot that goes into a "proper press". There's nothing "quick" about a proper pressing. I don't know everything involved, but I know humidifying the comic before the press is part of the process (and other parts of the process are simply "trade secrets" that take years of experience to learn). I also know that each of the different eras of comics (Gold, Silver, Bronze, etc...) require different methods (temp & time in the press).
I may be wrong but I believe a quick press is only a quick heatpress with no humidifying. After cooling down the paper fibers will want to revert to their pre-pressed state.
I can only say that the comics I have had "quick pressed", seem to look exactly the same when I get them back. Whereas the comics that have been properly pressed look really good.
This is all my Opinion, maybe others have had big success with the quick press. I just think if you're pressing looking for a bump in grade, just pay the extra money and have it done right.