This technology does exist on land however. Free Space Optics[1] has been around for a while but hasn't taken off in a big way because it's less reliable than sending light down a fibre cable, even though it is cheaper.
[1] http://en.wikipedia.org/wiki/Free-space_optical_communicatio...
Then you step outside to look up at the sky and you lose your eyesight
People think that lasers produce a parallel beam. They don't - they are diffraction limited by the width of the beam. The narrower the beam, the more it spreads out. For example, a 1cm wide beam produced by a perfect laser would spread out to around 20m wide when it hits the ground from 260 miles away. That's assuming visible green light - if it's infra-red (or even just red) then the spread will be wider.
This could be an incremental bandwidth (but not latency) upgrade over existing satellite internet service to remote areas (by transmitting to a single ground receiver that serves a local area), but that's about it.
That's not a fundamental limit. Existing satellites have high latency, because they're sited at insanely high altitude -- ~36,000 km (6 earth radii; 120 light-milliseconds (-> 240 ms minimum round trip)). This is for engineering and economic reasons which aren't solid: one, because geostationary [0] orbits allow dumb dishes that can't track moving objects; and two, because it allows small satellite networks -- i.e. one satellite covering a whole continent -- commensurate with the small size of the market.
If instead you had a network of satellites at say 500-1,000 km (unjustified guess), the latencies could be no worse than a direct optical fiber.
edit: Here's a sophisticated diagram, https://i.imgur.com/t1SOVpZ.png
[0] https://en.wikipedia.org/wiki/Geosynchronous_orbit#Geostatio...
There were plans for similar services, such as Teledesic, which went nowhere. I guess that enough land-based internet covers the majority of the target market, so there isn't enough market left over to justify the cost of a high speed satellite data provider. Remember, in LEO orbit, the satellites have to be replaced after about 5 years or so (atmospheric drag, and they run out of booster fuel).
Lower cost to launch via Space-x reusable rockets may change the cost equations though.
Speed of light: ~299,792 km / s Geostationary orbit distance from earth: ~35,786 km