I’ve always (like 6 months of study) thought it was unpredictable.
However, looking at your examples: could it be a question of the number of subsequent mora in the phrase? For example taihen where hen has 2 mora and daiji where ji has one mora. Likewise taisetsu, taikai However… daikon doesn’t fit the rule.
Ive come across it ONCE. Actually the reason I came across it was because a character pronounced it that way, which others found weird. In that case it wasn’t written in kanji either.
In short, no. だい is the older Go’on reading (The first readings that came to Japan, through Korea, from the Wu regions originally, while たい is the Kanon, the later readings from the Tang dynasty.
Aside from various strata of importation, a number of Go’on readings were replaced with their corresponding Kan’on readings, but it was incomplete, so you get this mess going on without much reason behind why certain words are how they are.
Part of the reason some are “dai” and some are “tai” is to differentiate from homonyms. If a tai reading jukugo has too many homonyms, typically the reading will be dai, and vice versa. Maybe not useful for beginners, but could be once you get more advanced.