How long does it take to break even on the carbon output of asphalt demolition and haul-away vs carbon input of optimal density trees planted in the same space?
I don't think it's fair to look at carbon output in isolation here. This would greatly help with a variety of issues such as mitigating urban heat islands, providing wildlife habitat, aiding pollinators, and just generally making the world we live in less hellish.
It's probably a pretty favorable comparison anyway. Asphalt is almost 100% recyclable. The demolition often just involves a single bobcat and a dump truck that hauls it to the recycling plant. A commonly used number is 10kg/tree/year for the first 20 years of a tree's growth so a plot with 25 trees would remove ~250kg/year. A gallon of gas releases about 10kg of CO2, so in that 20 year period, the little plot would capture about 5,000kg of CO2 or ~500 gallons equivalent.
Unmaintained asphalt eventually reverts to gravel. No need to haul anything away.
Were I replacing parking lots, I'd prioritize any abandoned / under utilized lots. Just start mulching and planting.
Plant willows and maples to break up the surface. Or maybe mechanically break things up, if the best-available-science supports doing so, if you're impatient.
Bonus Points: Convert planters, meridians, etc into P-Patch style community gardens. People love to garden. In my city, the wait list to join a P-Patch is years long.