Phasing out doesn't cause permanents to leave or re-enter the battlefield, so no "leaves the battlefield" or "enters the battlefield" abilities will trigger, and Kaito's first ability won't trigger again at the end of a turn in which he phased in
Rules and Clarifications Clarify existing rules if needed
Even after the companion mechanic got rebalanced, Lurrus proved too powerful for most formats that could easily match its deckbuilding requirement and turn it into a grindy value engine
Kabira Takedown and Sejiri Shelter are a bit more situationalthey might not be worthwhile if you're playing a deck with almost no creatures (which would be rare for a white-based deck), but they are worth playing in just about every deck with a reasonable number of creatures
Assuming that card draw is your best outcome, andlets be realit is, sacrificial enchantments are your best option
A sacrifice commander that bolsters its supply of sacrifice fodder via token production puts a lot of value in a tidy package, and I always appreciate card advantage in my command zone