I don't have a rigid singlespeed, but I do have a steel hardtail (Kona Explosif) with a 140mm fork and a 2.8" front tire. It's a total party bike. Prior to moving my parts over to the Kona from a Norco Torrent, I ran that Torrent with 2.8" tires front and rear.
You're absolutely right that the big tires, good brakes and more relaxed angles dramatically change the capabilities of the average hardtail or rigid bike. What we used to ride rigid in the early 90s are not at all the same bikes that people can ride now.
Too bad that more people don't start on these bikes; far too many just jump right into full suspension. In the old days, that's all we had and it made you a better rider by default.