UV light would penetrate clouds better.
Indeed, aiming the collimated beam would be a problem, but not an insurmountable one. Given the bandwidth benefits and the relatively small size of the transmitter (compared to microwave), many small (cheap) satellites could serve the same purpose as an Iridium constellation.
It wouldn't work indoors, but neither do satellite microwave links. The reason cell tower signals reach indoors is signal strength. It's prohibitively expensive to place equivalent transmitters into orbit.
* Clouds are a killer.
* Laser is highly focused - downlink would be tricky to support more than a couple of ground stations. Uplink would be extremely difficult because the uplink would have to track a (relatively) fast moving LEO satellite. Neither would lend themselves to a handheld ground station ("phone").
* Non-laser solutions likely don't have the bandwidth or the power to be effective.