If tri-ribs were a good idea on tractors used to mow lawns, then all the manufacturers would be putting them on. Turf tires were developed because they do the least amount of damage to grass. Tri-ribs are standard on the front of 2 wheel drive tractors used for farming applications because the ribs bite into the soil to make the tractor turn when it is pulling ground engaging attachments via the drawbar. As an example, there are some types of harrows that cannot be lifted off the ground so what do you do if you can't get the tractor to turn and you can't back up?
Yes the tri-ribs look cool and they also work well in snow or in the garden but they are tough on turf when sharp turns are made or the ground is soft or the soil conditions are sandy.
Sno-Hogs were designed for snow blowers to get away from chains. They are not as aggressive as tri-ribs but they are certainly more aggressive than the smooth, rounded turf tires.
Everyone's property comes with their own unique conditions. There is no such thing as the perfect tire but some work better than others do in all-around situations. Take a look at the Vredestein V-61 5 rib tires. You have to run tubes with the 16.00's but people who have bought these tires are very happy with them.