Why can no-one else see the complete injustice in this example of accusing a person based on a clothing alert?
Here is a fact - clothing spends most of its time NOT being worn. Probably 98% of its time. Just laying around in your house or flat. Have a look around your place and it proves it.
So before you even think of suspecting a person based on clothing alert you have to look at all the many possible scenarios that fit in that 98% where even if the alert were valid the person is completely innocent.
I can understand the pont of searching for alerts on clothing in certain cases, e.g., if a witness had seen a potential suspect wearing x,y, z on the night of a crime but who had denied ever having met the victim and who had stuffed blood-stained clothing with the victim's DNA in a garage or cellar, then that person would have some explaining to do.
In this instance, the exercise seems pointless.
It's possible that at some point the PJ thought that Kate had spent time cradling her dead child's body in her arms, wearing those clothes, along with CC, at some point between the end of tennis and going out for dinner and behaving totally normally.
Grime had presented the dogs' clothes sniffing capabilities as an option and the rest is history. The PJ may well have thought that that they'd hit the jackpot...