Hmmmm, two things:
1. If your doc/nurse said no treadmill, do what they say. You can contact them and say you feel great and would like to start on the treadmill, but it’s not a great start to unilaterally contradict your doc’s explicit recommendation. Sets you up for a bad precedent, because there are going to be a LOT of things in the next few months that the doc recommends and you don’t want to follow. The introduction of solid foods being a huge one - most people struggle with feeling just fine and ready to eat, granting yourself a hall pass early is just going to start you down a slippery slope.
That said...
2. Everyone’s doc is different. I didn’t have any explicit restrictions on exercise, and while I didn’t go on a treadmill, I do live in a city and was easily walking three or 4 miles a day going from client to client by nine days out. So I won’t say it’s across the board a bad idea, just that your doctor may have very specific reasons for saying you shouldn’t be on a treadmill.