And there you hit the mark with the phaser/laser props, too.
Remember that the ones we are discussing had one very prominent feature - multiple barrels or firing chambers that were rotated into position? The rifle had just one barrel but three identical-looking chambers; the sidearm had three stubby barrels of differing lengths and diameters.
Looks and sounds like a multi-function weapon to me. One barrel fires stun phaser beams, another fires kill phaser beams, and the third is the ever-handy extra, the cutting laser...
Separate barrels for stun and kill reappear in STXI. And while the standard phaser is the preferred tool for cutting in "The Naked Time" already, note that this weapon, too, appears to have two cylindrar barrels - one within the other!
My preferred excuse here thus is that in the 2240s, the standard sidearm carried a few extra functions, but increasing integration replaced this with just two barrels in the (alternate?) 2250s and (or?) with just one multi-function contraption in the 2260s, and the additional complexity of the laser barrel was either ditched as counterproductive, or integrated into the standard sidearm. The 2250s rifle with three different functions / firing chambers was simplified at the same time and the older model went quite out of fashion. OTOH, much like its 24th century counterparts, it had never really been more powerful than the heavy sidearm versions. It had merely had certain bells and whistles also quoted in the DS9 era: multitargeting, gyrostabilizing and whatnot.