Except when not a single ultimate pet works that way. Tibbers stays, Maiden of the Mists stays, whatever the fuck Mordekaiser has at that moment stays. So saying you think it's a "good system" when that system doesn't actually exist is a kind of an odd to say.
you're talking semantics so that's useless. ivern's ult works that way, so whatever, i'm discussing this as a system. you're the one who says hates when i pick apart ur points, so don't do it urself
the rest is debatable, just because other pet champions work like that doesn't mean that ivern should, most other pet ults have extra effects that make the actual pet relatively less important compared to daisy. maiden is 5x more useful when yorick is around, tibbers does massive aoe dmg and cc, etc. daisy just walks around and hits people, her capabilities don't change much if ivern's alive or dead, so it's not the same thing as tibbers, who people mostly ignore or see as free 50g when he's alive
and also it's worth questioning if it's fine that other pet ults work that way.