Clever idea honestly. At one point you might even wonder why having roads at all, as everything could be potentially done underground. Then all highways etc could be transformed to bicycle lanes, or even just given back to nature. What an amazing transformation would that be.
All changes impact nature, only questions of how much, what’s impact, etc — and my guess in the impact of tunnels is poorly understood. While not tunnels, hydraulic fracturing ("fracking") to known to increase earthquakes. Another likely impact would be any vibrations that reach any organisms able to sense them, which might in turn change the behavior on organisms above the ground.