What you are saying is basically that it's better to fire a fatal gunshot because using a taser is too painful!
Well, yes, if it takes one gunshot but a lifetime of constant tasering to keep the assassin from completing the crime she cannot stop committing.
It's apparently well within Starfleet regulations to fire mercy shots to execute a defeated enemy; Kirk does it in STXI and ST3, but Picard and Janeway also engage in lots of it when facing the Borg. Yuta is a pretty good match for the Borg, a gift that keeps on giving unless put down for good.
Are you SERIOUS?
A phaser hit on heavy stun for ten seconds. She goes down in pain, she gets arrested, beamed to the Enterprise and is perfectly fine the next day. But instead you vote to KILL HER?
Timo, that's pretty fucked up. If that happened today, what would you think? Imagine the newspaper headline...
Police officer shoots dead armed suspect because taser was deemed too painful.
A 30 year old woman was shot dead today. Witness say that pepper spray had been used but had only limited effectiveness. Another police officer had used a taser, which left the suspect unable to move, but a malfunction had caused the taser to fire at reduced capacity. After the taser discharge had finished, another police officer drew his weapon and fired a single shot, hitting the woman in the head and killing her instantly. He had a taser which was working perfectly, however he chose to use lethal force instead. When asked why he chose this course of action, the officer said, "In my opinion, the taser was painful and I didn't want to subject the suspect to that level of pain."
What would you think of that?
Seriously, how fucked up must you be if you think that ending a life is a better choice than inflicting temporary, non-lethal pain? Or do you think that the ONLY OPTION is to keep shooting her with a phaser on stun for the rest of her life? They do have PRISONS that are kinda hard to get out of, you know!