From DS9: Return to Grace:
KIRA: This is a standard issue, Cardassian phase-disruptor rifle. It has a four point seven megajoule power capacity, three millisecond recharge two beam settings.
ZIYAL: How do you know so much about Cardassian weapons?
KIRA: We captured a lot of them during the occupation. It's a good weapon, solid, simple. You can drag it through the mud and it'll still fire. Now this. (Federation phaser rifle.) This is an entirely different animal. Federation standard issue. It's a little less powerful, but it's got a more options. Sixteen beam settings. Fully autonomous recharge, multiple target acquisition, gyro stabilised, the works. It's a little more complicated, so it's not as good a field weapon. Too many things can go wrong with it.
While a log system on a phaser would have its benefits, it would also have its drawbacks. Let's picture a Starfleet phaser with a mandatory logging feature. In order to be mandatory, it would have to be tamper-resistant; otherwise, an officer like Riker could easily enough disable or alter the logging to cover his tracks.
These phasers are also meant to serve as battlefield sidearms. For the logging system to have any integrity, attempts to interfere with logging would almost certainly have to render the phaser useless. In Kira's frame of reference, that represents one more thing that can go wrong with it, potentially fatally to the phaser's legitimate user.