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For one thing, there have been reports, nowhere contradicted, that Zimmerman was not tested for substances and that such tests are standard practice.

Nowhere was it reported that Zimmerman was anything but lucid and sober, particularly given his wherewithal during the non-emergency police call, and the coherence of the contemporaneous statements he made just after the event. I am personally aware of many cases in which no tests were conducted after a shooting. Nonetheless, remember that the police may not "test for substances" without consent or a warrant. I have seen no waiver signed by Zimmerman consenting to such tests, nor have I seen a warrant to conduct them without his consent. Notwithstanding all the above, it may yet be revealed that tests were indeed conducted either subsequent to a warrant or with Zimmerman's consent.

the initial report has him arrested (or detained if you like, or charged in a preliminary manner) with negligent homicide or manslaughter (I saw that on the pdf of the police report);

The "charge" listed upon the police report is the title given to the event because that is the matter under investigation, and the police know that if evidence were uncovered implicating Zimmerman, that was the most likely charge. If I respond to your home and you tell me PERSON A robbed you, and your story is just plain crazy and appears to have no merit, I am still going to take a police report for ROBBERY because that is the matter being investigated. A police report is not a charging document or criminal complaint.

and for such a charge one might reasonably expect a more thorough inquiry than has been described in all reports.

Detectives interviewed witnesses and took their statements, Zimmerman was transported to the police station and questioned, the crime scene was secured by crime scene tape and guarded by three officers while crime scene technicians collected evidence, Zimmerman's firearm was taken as evidence and retained by the police, and the police submitted a report of the event to the prosecutor for consideration of the titled event.

I'm not sure how much more you'd expect. That's a pretty standard investigation.

one witness claims that she had to persist in requests to give her statement

The Sanford police have stated this is not true.

By the way, I don't hear Zimmerman's lawyer claiming that no further investigation is necessary. If that were the case, surely he'd be saying so.

I suspect Zimmerman's attorney knows by this point that no legitimate investigation will uncover evidence substantiating charges, much less a conviction.