Why are laser signals used for long-distance communication transmitted at such a low power level?
Because they can, and at least for now, because they must.
In addition to increased data rate, key reasons for investigating using laser communications for spacecraft are reduced mass, reduced power consumption, and reduced volume compared to radio communications. Using high-power lasers rather than low-power lasers would defeat these purposes.
Using laser communications for spacecraft of any power level comes at a cost compared to using radio communications. A radio communications system between a spacecraft near the Moon and the Earth requires sub-degree pointing accuracy on the part of the spacecraft. That is easily attainable. A laser communications system would require pointing accuracy at the arc second level. That's getting close to spy satellite or Hubble level pointing accuracy. Most spacecraft do not need this kind of pointing accuracy for their instruments.
This increased level of pointing accuracy needed for laser-based communications does not come cheap in dollars, mass, power, or volume. This in turn makes the reduced mass, power, and volume requirements of a laser communications system be offset somewhat by the increased mass, power, and volume requirements needed for pointing accuracy. A laser-based communication system must necessarily operate at significantly lower power levels than a radio-based communication system to be competitive with that radio-based communication system in terms of dollars, mass, power, and volume.
Finally, at least for now, laser-based communication systems have been auxiliary test articles on operational satellites, or primary systems on low-cost experimental satellites. While space agencies do spend monies on experimental vehicles, they don't spend a lot. In both cases, the money, mass, power, and volume needed for a high-power laser-based communication system just is not there. The experimental systems to date have all used relatively low-power lasers, as do the operational systems planned for the future.