As a father of two I would say "nope", primarily because you won't be deciding the rhythm. Best you can do is coordinate sleep with your partner so that there's at least one somewhat functioning parent at all times.

As I'm typing this my 1.5yo is napping. I had maybe 6h of sleep but I'm after (part time) work and at home already, so I should probably nap as well.

Can't. My adult body won't go to sleep right now even though I'm feeling drowsy because it's too bright, too loud and chiefly I already had too much caffeine in the morning and I have like 15 minutes until I'll have to head out to collect my older child from preschool.

My SO is knocked out cold at the moment though, so I'll be relying on her this evening.

I have a similar natural rhythm, or I should say "had". For the first year, especially the first few months, it was a godsend (for my wife, especially), but now that we're in a fairly consistent sleep routine with our two year old (~8pm-7am), I've shifted to something more like 8pm-1am out of necessity.

Although... I was up until 4am and got up at 6:30am and feel surprisingly great, so it still happens from time to time. :)