Yeah I guess in theory you could just go to the theatre and buy tickets, we've done that in London before when we were walking past a theatre and realised a show was going to start in 20 minutes.
We'd made our minds up on which show in New York we definitely wanted to see and also wanted specific seats, so I booked.
That reminds me, when I was looking I didn't realise the seating areas were named differently - in the UK - The Orchestra is literally where the Orchestra sit and play!! I was quite confused at first and thought - blimey thats a large area for the Orchestra

Our seating areas are called Stalls = America Orchestra, Circle = America Front Mezzanine and Upper Circle = America Rear Mezzanine.