How common is it for law enforcement to investigate wire transfer transactions?

No. It is not. In most cases, wire transfers are usually investigated by the compliance and/or investigative units within the bank. In the event, the bank seems a crime has been committed the compliance department has a legal responsibility to report it to the relevant authorities. The LEAs (Law Enforcement Agencies) then determine on how to investigate it further, (if at all), based on the information provided by the bank, or the related financial/non-financial institution. But it is not common for Police to investigate money wire transfers. This usually comes under the White-Collar Crimes and there, within such LEAs is a dedicated unit (usually) that can further handle this case.