Sci-fi time: Do laser pistols make sense?

The laser pistol (or similar personal directed energy weapon) is a staple of science fiction, and you can imagine why:  No pesky ammunition to carry, possible some really cool light/sound effects, near-speed-of-light to target (though phasers and blasters and the like are often shown in TV and movies with laughably slow velocities, so the audience can see the beam or pulse propagate*).  Still, does a laser pistol make sense as a practical weapon?  This isn't "nano", but it does lead to some interesting science and engineering.

I'm a complete amateur at this topic, but it seems to me that for a weapon you'd care about two things:  Total energy transferred to the target in one shot, and the power density (energy per area per time).  The former is somewhat obvious - you need to dump energy into the target to break bonds, rip through armor or clothing, etc.  The latter is a bit more subtle, but it makes sense.  Spreading the energy transfer out over a long time or a big area is surely going to lessen the damage done.  Think about slapping a board vs. a short, sharp karate chop.

From the internet we can learn that a typical sidearm 9mm bullet has, in round numbers, a velocity of about 400 m/s and a kinetic energy of about 550 J.  If at bullet stops about 10 cm into a target, you can use freshman physics (assuming uniform deceleration) to find that the stopping time is half a millisecond, meaning that the average power is 1.1 megawatts (!).

So, for a laser pistol to be comparable, you'd want it to transfer about 550 J of energy, with an average power of 1.1 MW spread over a beam the size of a 9 mm bullet.  Energy-storage-wise, that's not crazy for a portable system - a 1 kg Li-ion battery when fully charged would contain enough energy for several hundred shots.  Batteries are not really equipped for MW power rates, though, so somehow the energy would probably have to be delivered to the beam-producing component by some exotic supercapacitor.  (Remember the whine as a camera flash charges up?  That's a capacitor charging to deliver a high-wattage pulse to the flash bulb.)  The numbers for portability there don't look so good there - megawatt power transfers would likely require many liters of volume (or interchangeable, many kg of mass).   Of course, you could start with a slower optical pulse and compress it - that's how facilities like the Texas Petawatt Laser work.  Fascinating science, and it does get you to ~ 100 J pulses that last ~ 100 femtoseconds (!!).  Still, that requires a room full of complicated equipment.  Not exactly portable.  Ahh well.  Interesting to learn about, anyway.

(*The beam weapons in sci-fi movies and TV are generally classic plot devices:  They move at whatever speed and have whatever properties are required to advance the story.  Phasers on Star Trek can disintegrate targets completely, yet somehow their effects stop at the floor, and don't liberate H-bomb quantities of energy.  The stories are still fun, though.)