My dd stays up late often- all night sometimes- so we do stuff at night regularly. She woke up at 9:30 PM yesterday and is still awake at 5AM today. She'' probably go to sleep around noon or 1 PM. My dd sleeps 10 to 12 hours from the time she goes to sleep regardless of it it is 7 PM, midnight or noon.
I have never purposefully kept her awake when she was tired because I wanted to do something- it is just her natural body rhythym. I don't think it would be right to keep your child awake if they are tired. Following your child's lead on when they go to sleep though is fine IMO as long as it works for your family.
We've taken dd out shopping late at night and no one has ever said a word to us. I think the judgemental people are at home asleep.

Some drawbacks to the habit of late nights:
Less time to play outside before it gets dark or mosquitoes come out- have to be quiet outside so sleeping neighbors aren't bothered
Not as easy to do stuff with kids/families who go to bed earlier or get up earlier- might miss some kid activities
Have to be careful of grazing at night- keep regular meal times even if the hours are at night
Different sleep schedules for different family members can be tough to handle sometimes. My dh has to get up early for work so he goes to bed at 10ish. If we stay up later we have to be quiet so he can sleep. I also miss sleeping at the same time as him.
Harder for adult to adjust to some late nights and then some regular days than for the child- at least for us. That can lead to grumpy or lethargic parent. Honestly, my dd's late nights are hardest on me.
Use more electricity.
Positives:
Following natural body rhythym so less struggle over bedtime
Less tied to a traditional routine
See cool things at night- stars, moon, different bugs, nocturnal animals
We can do lots of things at any time- cook, crafts, reading, play games, do puzzles, watch DVD's, the internet is always open
In summer we are more active when it is cooler.
More places are open late or 24 hours these days.
Less crowded shopping at night.