Not the most comprehensive nor robust test, but I'll like to share my findings anyway.
If you enter old transfers that had HTWT 0 from SWSH into HOME, this is the distribution of the HTWT reroll.

Out of 3,720 Pokémon:
2 had HT 0
1 had WT 0
2 had WT 255

Certainly gives hope.. pic.twitter.com/4sHQ8bASaj

— theSLAYER (@QStheSLAYER) June 11, 2023