@puputanidya
They only talked about bring note to allies if I remember correctly. She hadn't said specifically who will be first or second. He hasn't known which ones she would bring to and when she would bring it to them.
Going bold could be backfired on his reputation. She could have hidden on herself, her room or somewhere else that they don't even know.
If they are catching would be solid evident, yes, but, the stake is very high. It means his reputation would be gone from his 'accusation'. If star bearers reported Edward for abusing his authority.
Kate is pretty sharp. Edward knows this from debut examination. if Kate noticed and were being careful like in debut, he and star bearers might not stand a chance.
And that scenario would work if star bearers would even work for him after his empty word.
No matter it was the truth or not, They would doubt on his bold statement. Even with all of his explaination, it is still a word. For them, it's probably a good theory at the best.
Also, They don't have a close relationship. The willing to do is pretty much low begin with.
If the search failed, Star bearers' and Edward's reputation could be massive blown and Kate's favor would be raised. After all, no matter moves they used, I believe it would have gained some attention by bystanders.
Although, whatever the search is successful or not. It depends on method, timing and how clever Kate is. It's matter of debate which would lead to no end. The risks I have mention would make it less willing to do.
Also, Edward want to go 3rd floor so badly. He can't really risk his reputation like that. That is why he was going roundabout way. So, accusation won't blow back badly on him.
This way, the star bearers would have value him less. But, that is about it.
Like I said before he forgot about Kate, only remember her again because of Maryrose and their inability to capture Barbara red handed.
That is what I mean by leaving the matter to star bearers. He just waited for star bearers to report the result. You could say that he forget by not doing anything else.
I mean, I don't think he have anything else to do on this beside using his authority.
Sorry, if I wasn't clear enough.