You're exactly right, non-speedbuilding tournaments don't force anyone to speedbuild, but those who are short on time (whether it be to IRL or other forums happenings), may be more inclined to speedbuild their decks, due to having less time beforehand. The TOs figured that War would spread this effect greatly among the community, and thus, we defaulted to speedbuilding. We could have ran non-speedbuilding ones, however, this may cause an "unfair" setting, as those in War will have less time to analyze tourney meta when faced with non-speedbuilding, due to the aforementioned time constraints of War. By forcing speedbuilding, we put everyone on a "level" playing field, as far as deckbuilding time is concerned, as rules aren't predetermined.
Some individual opinions may vary between TOs, but the core sentiment should be the same. Apologies for fragmented ideas, phone at 1% and I'm not home.