DS really was there from "day dot" wasn't he. He will have known all about the DV, drugs, SS involvement, SH's record, Tia's living arrangments etc.
Personally, I would not, and did not wear a t shirt when my sis was missing in the says before she was found dead - why not? Because everyone who knew me and everyone in the community already knew she was missing.
The people who didn't know me - could they read what is on that t-shirt unless they were close up? If you are close enough to a person, you can talk to them. You would carry a large and recent photograph on a flyer to hand out. (Assuming that the police think this is a good idea) People can take it away and keep it - it gives them something real to have and makes them think actively rather than passively about the missing child. You and talk to everyone in pubs, clubs, restaurants, shopping centres in the early days. Once it has national media coverage, you don't need t-shirts.
They were making it about them imho, or maybe, DS was assisting the police all along. Could be that he assisted the police in a covert way. I really hope so.
Although I have experience of a family member missing and being found dead, perhaps it is because I am from a different background that I cannot relate to any of the behaviour of this family since Tia "went missing". They were behaving as though she was already dead and they wanted to be grieving and seen to be grieving. No one in my entire family shed a tear until sis's body was found. It wastes time when you could be doing something useful.
Just my opinion and absolutely no offence meant to anyone who thinks differently.