I didn't see you post before writing the above or I would have incorporated it into my answer. Well, for a start, I wouldn't just take a person and try to fit the case around them to see how that would work. I have seen that happen so many times. I am not very much liked or appreciated for my views, I can tell you that. But, I would rather step on toes here than have someone who had nothing to do with this have their life poured out on these pages in an unwarrented way. Think like LE. If this were your case, how would you conduct it? Then act accordingly. That is the best adivice I could give you.
But, hey, I am in retail so what do I know.
To sincerely respond:
I'm not trained detective and don't know what they would do - lol the only info I have gotten on methods was crime shows like Prime Suspect or NYPD or etc. It seems the lead detective will assign the others to specific areas. I don't want to be redundant. It's you follow up on so and so, you run the plates, etc. So that doesn't mean the det. is out to get anyone, they are out to try to figure out if person(s) of interest have alibis, what were their actions before, after the murder, etc. I guess the point of what you are saying is "unwarranted", I am guessing you are referring to what you feel might be unwarranted criticism of DT, CPC, SP, etc? There is a diff., I think, in name-calling a person, just picking on them as a person, or taking a good hard look and maybe questioning motives or activities.
After all, if there is no solid evidence of substance (hairs, prints, DNA) what choice does one have other than be trained on timelines, lifestyles, behaviors, influences, discrepancies in testimonies, other things that "don't make sense"? One reason I come back to these persons is there aren't any OTHER persons who can be reasonably connected where there is information to fit them into a profile or a timeline, etc.
People come on here and say they looked at so-and-so, he/she looks like a low-life, acted hinky, gave them the creeps, etc. Ted Bundy didn't give anybody the creeps and look what he did. It's not right to convict anyone on face value but one has to look somewhere.
It's kind of tricky and what comes to mind is, say a crime is commited and there were several people of different races and mixtures there. A white person reports a person who is black and says he looked shifty-eyed and nervous, etc., how else are you going to differentiate the person from the others in the crowd? Then you are called a racist who automatically targed that person as guilty?