Latency is a real problem. Distances to satellites in orbit are very long. Also, there is a scalability problem. How many ground targets can a satellite simultaneously provide service to? My guess is, not a lot.
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.
What you're describing is essentially a data version what the Iridium network provides. Iridium is a constellation of 66 satellites at 450 miles up. Unfortunately, when Iridium was launched, forward thinking wasn't part of the plan -- data is stuck at around ancient dialup modem speeds.
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.
If you're talking lasers though, don't forget to factor in the time needed to reacquire a new satellite in once the existing one goes over the horizon. The shorter the orbit, the more often you'd have to do this.
If they had a way to have almost unlimited ground targets (maybe using a rotating mirror, or something like https://www.kickstarter.com/projects/117421627/the-peachy-pr...), I could deal with the not so bad ~240ms lag for most of my communications (if you aren't gaming), especially if it's faster then my slow cable connection....
Speed of light: ~299,792 km / s
Geostationary orbit distance from earth: ~35,786 km
A grid of sats designing for blanketing the earth in comms is going to be at most 400 miles up, most of my packets go way further than 800 miles, so no, latency won't be an issue.
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.