Point shooters like to use police-compiled statistics of officer-involved shooters to make their case. Because NYPD stats are often used, I went over that first. Here are some stats from Los Angeles Police Department.
Quarterly Use of Force Report for the First Quarter of 2012
Officer-involved shooting incidents (not including animal shootings) made up approximately 55 percent of all Categorical Use of Force incidents in 2011, a markedly higher proportion than in previous years. As noted above, hit shootings grew at a much faster rate than did no-hit shootings, but this seems to be a ratio adjustment from 2010, which showed an unusually low hit proportion of 65 percent. In most years, about 75 percent of reported LAPD officer-involved shootings result in a person being hit, as they did in 2011. About 41 percent of all shootings in 2011 resulted in the death of the subject.
LAPD 2010 Use of Force Annual Report
Page 16 (PDF 19)
LAPD hit/no hit ratio of Officer Involved Shootings is between 65-75%
Page 20 (PDF 23)
63% of all LAPD Officer Involved Shootings took place at 21 feet (7 yards) and further. If they had only trained in point shooting techniques and never past 21 feet, these officers would have been ineffective in almost two thirds of these incidents.
Within the ranges where point shooting is potentially most effective (inside 5 yards or so), 22% of LAPD Officer Involved Shootings in 2010 took place. In that same year, 30% of LAPD officers engaged at over 15 yards.
How does this compare to the NYPD?
NYPD Annual Firearms Discharge Report 2011
On Page 24 (PDF 42)
In 2011 47% of NYPD officer involved shootings took place at 6 yards and further, with 38% from 6-15 yards and 9% at 16 yards or more.