Let's remember that TOS "Devil in the Dark" told us that civilian miners had access to Type 1, while the more potent Type 2 apparently was Starfleet issue only. So back in the 2260s at least, Type 1 wasn't some sort of an ultra-special, concealed-carry device for professional killers, but rather the everyman handgun of choice.
TNG Tech Manual information on phasers suggests that Type 1 could be handed out with abandon because it can be locked on a mode where only settings from 1 through 3, light to heavy stun, are available. The book also suggests officers get assigned Type 1 guns as personal sidearms (so supposedly Riker or Bashir or Kim always has one in his cabin, waiting for use), whilst Type 2 phasers are dished out as needed in alert situations or when preparing for away missions. This might not be in good accordance with evidence from TNG itself, where it's not trivial for even a Starfleet officer to gain access to a phaser of any sort (say, "11001001").
Timo Saloniemi