Actually I am all for this.
Considering that LEOs are reactionary by and large, using force escalation as needed...
And considering we have way too many psychologists and psychiatrists already... Sure... Throw that shrink forward at a ranting criminal crackhead... It will give the cop a second to get his feet set.
And against a true criminal... I know a shrink is generally not thick protection... But about anything helps to slow the bullets down...