Another point to remember is that had the suspect been identified after being committed to an asylum, that evidence would effectively have been useless because a person "deemed insane" could not be put to trial.
Regardless of what order the identification and the asylum committal came in, wouldn't it have been worthwhile taking Kosminski into a court, in order to ensure that he went to Broadmoor rather than Colney Hatch? It wouldn't have been necessary to put Kosminski on trial - Thomas Cutbush was found unfit to plead, but was still sent to Broadmoor rather than Colney Hatch.
That's an interesting thought Robert. What was the actual verdict with Cutbush? Since Broadmoor was for criminal lunatics, was he found "guilty, but insane" or something like that? I think, in the case of Cutbush, the evidence was compelling, whereas without testimony from an eyewitness, bringing Kosminski before a court would have risked an acquittal. In that case the suspect might have escaped incarceration altogether. That's just one thing that comes to mind. Does that make sense? Clearly, without that supposed eyewitness testimony, the police didn't think they had enough to charge Kosminski, and even watching him "by day and night" (assuming it was Kosminski they were watching), they risked letting someone they believed to be a murderer kill again. I'm afraid I'll never be able to come up with a clear enough picture of this suspect and the events surrounding him to satisfy even my own "biased" beliefs. Won't stop me from trying though!