Its major advantage over the previously practised "classic" technique is that it allows the skater to do useful work during the part of the stride that was "wasted", and therefore to go faster.
Wheels used in speed skating are usually round or elliptical in profile, and do not literally have edges.
The principal advantage of the double push is that it allows skaters to generate propulsive force during a part of the stroke cycle which was previously wasted.
In the glide phase of the classic stroke, friction from road, atmosphere and bearings tends to slow skaters down, yet the deep knee flexion during this part of the cycle fatigues the muscles.
This is beneficial to their muscles and also helps keep speed more nearly constant instead of surging ahead and then slowing down repeatedly.
One of the best ways to go faster is to push further in each stroke, but whereas traditionally this requires sitting lower (restricting blood flow and increasing lactic acid production in the muscles), in DP the same leg at a higher bend angle can achieve a longer effective stroke by pushing both inward and outwards.
Chad Hedrick, due to his success in connection with the DP, has had his form widely commented on since he moved to ice.
Perhaps some technical developments could enable creating an ice speed skate that can carve, but it may have more drag.