reason for using the SWAT

First, a brief story:

A 44 year old male diagnosed for many years as a paranoid
schizophrenic was shot and killed by police during an attempt by a
SWAT team to remove him from the bedroom where he had barricaded
himself for two days.  He was extremely paranoid of police, had
delusions that police were plotting to kill him, and had previous
encounters with local police in which he assaulted and injured at
least one of them.  He was considered a danger to himself and others
by psychiatrists.  A psychiatrist had failed in negotiations over
several hours to get him to come out voluntarily before police were
finally called in.  An ambulance was staged on the street during the
standoff in order to transport him once he was in custody.  The plan
was for the SWAT team to spray tear gas into the room, thereby
blinding and disabling him, and then storm the room and physically
overpower him and take him into custody.  It was known in advance that
he had axes and knives in the room and was likely to use them on
anyone who entered.  That is the reason for using the SWAT team.
Unfortunately, during the assault by the SWAT team he swung an axe at
one officer and another officer fired in defense.  He was shot once in
the abdomen and died later at the hospital.

First, let me say that I do *not* wish to debate the rightness or
wrongness of the use of lethal force in such cases.  That's a very
long, very boring argument that no one ever finishes and there is no
shortage of better cases to debate than this one.

What puzzles me is this: Extremely dangerous animals are captured
routinely with little risk to the animal or capturers via the use of
tranquilizer darts fired from air rifles.  Why is this technique not
employed in cases like this? (ie, someone who is quite dangerous but
who is not a criminal.)  Are there medical, legal, or law enforcement
reasons for not using such an approach?  It seems simple and obvious
to me, but perhaps I'm missing something.

Your thoughts appreciated.