Kiddushin. He did not say “to me” VS Your daughter is consecrated to me

Why didn’t he tell me, “You are sanctified,” according to most opinions, one is not afraid of sanctification,
Compared to the one who says, “Your daughter is consecrated to me” – are they afraid of consecration in relation to all the sisters?
 
The reason why in the second case they are afraid of Kiddushin is that there was an “act of Kiddushin.”
Husband – who said and gave. In relation to the wife – the act was delimited (in relation to all the daughters of the family), at most it was not precisely defined in relation to any of them, and therefore they are all afraid.
In the first case, too, all the actors were in the play. Only the opposite.
A specific woman – to whom the act of consecration was directed. Regarding the husband, the act was not precisely defined in relation to whom it was consecrated, since he did not say “to me.”
But it is limited to a limited number of people! (Similar to nurses).
Because, in any case, there is a man here who gave and said. At most, another option is that someone made him a messenger of Kiddushin, and this can be ascertained through him.
Or at least a suspicion that the act of sanctification is sufficient, perhaps he is the one who sanctified and not the one who sent.