The obvious problem is finding a suitable parking lot. Most parking lots are privately owned, and that means the owner is liable and at risk for what goes on. I don't like it either, but even an amenable lot-owner can get screwed.
I've ridden my XR100 on the street and in private lots, but I wouldn't try this without permission that would be impossible to obtain. Usually, I'll head out to a dry creek bed or some dirt lot under an overpass for some after-work riding, but only if I can't get out to a real park.
Riding in Urban brownfields is a major issue with the dirt bike community (something MO doesn't devote itself to much anymore). It seems harmless and responsible dirt riders would love the opportunity, but often times neighbors, politicians, lawyers, and other fun-spoilers try to impose on these fun loving people with stupid sensibilities and practicalities and stuff, and basically say it can't be done.
Unfortunately most people don't live near enough a motorcycle park or open public land that they can go for a ride with a couple hours after work or school. For most people, dirt riding involves loading up the bikes, traveling, and a whole-day destination.
I'm lucky to have an awesome bike park within 1 hour's drive. Hollister Hills has tons of great tracks and miles of trail. This California State park is 10 times better than any parking lot, but it didn't always used to be a State park.
Hollister Hills used to belong to Howard Harris -- of the Harris Ranch (California's largest cattle/beef operation). I understand the State had to take over because there was no way Harris could manage the liability of the operation once the environment turned litigous.
For road racing, private tracks are somewhat more practical because they can generate more revenue to pay massive insurance bills, lawyers, etc. Most people are willing to pay a couple hundred bucks for a trackday or race fees. Track day, school, and race organizers pay the track thousands of dollars. We wouldn't think of paying these kinds of fees to ride a mini-bike in a dirt lot.
It's pretty sad when you think about it. It's damn near impossible to ride your motorcycle anywhere unless either you own the land or the goverment gives you permission.