Having been in New York for 5 years, I can say that Rao's is nearly impossible, and Babbo has so many constraints that makes it appear impossible. But I feel like Per Se isn't really that hard, since it's open for lunch and it has the exact same menu as dinner.
For example, my brother came down to New York last month without any reservations on Thursday, and he was able to get us a table (6 of us) at Per Se's private dining room for that Sunday (for luch at 12:30pm). What's more, when we got there even the main dining room wasn't full!
Is this common? Or were we just really lucky?