The problem with AAA battery powered tail lights is the lumen ratings are very low, at about 50 lumens; whereas with a non-replaceable lithium battery tail light you can get upwards of 300 lumens. My taillights have rubber straps which make it easy to take them off, bring them in, and charge them, just like I do with my headlights. My best taillight is the Nite Rider Omega 300, the newer model is called the Omega 330, the numbers represent the lumens, this light has a variety of modes, and needless to say it's extremely bright in the brightest settings. But you are correct about the LED's lasting longer than the non-replaceable battery will last, which I think is insane that we can't replace those batteries when they'll no longer take a charge. 99% of all headlights use non-replaceable batteries as well, crazy, just crazy.

Planet Bike Superflash that costs around $25 uses a AAA battery, it's not very bright, but it does work; it's a old design that has been around for a long time because people, like you, want a taillight that runs off of standard batteries. There might be a couple of other AAA lights but I could not locate one in a brief search.