Still, in cases merely of suspected murder, or in cases where no evidence is taken, it would be manifestly unfair arbitrarily to assign motives for the deed, if deed it was.

No, one must start with the assumption, sufficiently accurate under all the circumstances, that the killings in which the killer is caught are fairly representative of killings as a whole.
All crimes naturally tend to divide themselves into two classes--crimes against property and crimes against the person, each class having an entirely different assortment of reasons for their commission.
There can be practically but one motive for theft, burglary, or robbery.
It is, of course, conceivable that such crimes might be perpetrated for revenge--to deprive the victim of some highly prized possession.

But in the main there is only one object--unlawful gain.

So, too, blackmail, extortion, and kidnapping are all the products of the desire for "easy money." But, unquestionably, this is the reason for murder in comparatively few cases.
The usual motive for crimes against the person--assault, manslaughter, mayhem, murder, etc .-- is the desire to punish, or be avenged upon another by inflicting personal pain upon him or by depriving him of his most valuable asset--life.

And this desire for retaliation or revenge generally grows out of a recent humiliation received at the hands of the other person, a real or fancied wrong to oneself, a member of one's family, or one's property.