"Keep your phasers on stun. And stay calm. I don't want anyone getting
nervous and shooting one of us by mistake." – Michael Eddington, 2371
They set phasers to stun, because it's like saying check your gun and make sure you have the safety off or on. They don't want to attack and cause more damage than they are suppose to until the situation is clearly against them. Also, if someone friendly fires and the phaser is set at stun, the most that will happen is that the person will lose a couple of brain cells. I don't know if phasers have a off button, but if they do they are probably saying make sure your gun is ready to go, make sure it is on.
Some directed energy weapons did not have a stun yield setting. Some
had only two settings, the stun and the kill setting. (ENT: "Broken
Bow", "Cease Fire") On phaser weaponry used by Starfleet in the 23rd
and 24th centuries, there were several different levels of stun
settings. Starfleet regulations stated that phasers were to be locked
at the level one stun setting. (TNG: "Aquiel")
From another site.
11. "SET PHASERS TO STUN"
It was established early on in Star Trek: The Original Series that the phasers used by the > crew of USS
Enterprise had a “stun” setting (as mentioned in “The Man Trap”
episode), and both Kirk and Spock often found themselves instructing
their crewmates to use the non-lethal capabilities of their
standard-issue weapons. However, it wasn't until the second season of
Star Trek: The Animated Series that we first heard Kirk issue the
command “Set phasers to stun.” The line eventually became an
oft-repeated order in subsequent series, turning up in both Star Trek:
Deep Space Nine and Star Trek: The Next Generation, as well as many of
the movies (including 2009's reboot).
From the wikia.
The first stun setting was called the "low stun setting", (TNG: "Force
of Nature") "setting number one" and the "base cycle stunning force".
(TOS: "The Enemy Within") A hit from this most minimal setting only
left the target dazed, unable to stand and think straight for a short
time. (TOS: "The Man Trap") Two phasers set on setting one fired
simultaneously could break large objects into pieces, such as the urns
of the second planet of the Taurean system. (TAS: "The Lorelei
Signal") In the 2290s, a phaser fired on stun did not set off internal
alarms on Starfleet starships. (Star Trek VI: The Undiscovered
Also, stun probably was the main setting. Why would Starfleet have their main setting anything higher, they are suppose to help, protect and do as little damage as possible.Telling people to set their guns at stuns, is also like saying make sure the situation needs higher force before you used the kill setting. And it might have been like someone saying "get your head in the game".
You don't know the situation. The place you go into might have kids or someone else very innocent. And you can still hurt them from the stun.
To some more vulnerable species, even the stun setting was potentially
lethal, for example the Trill symbionts. (DS9: "Invasive Procedures")
When used at close range, a phaser set on stun was capable of inducing
sufficient trauma to kill a Human, if fired at a vital organ such as
the brain. (Star Trek VI: The Undiscovered Country)
About the kill setting.