The EU duty cycle is actually averaged over an hour, not over a full day. In the USA there is no such duty cycle.
I never really understood why everyone mentions a number of end devices a network can handle. Gateway manufacturers do it, network operators do it and I'm pretty sure TTN did it too. These numbers are estimates that rely on tens of assumptions, so in my opinion it's very misleading. If you find any reference to a number on our website or documentation, please let me know, then I'll make sure it's removed asap.
The most important assumption in those calculations is that most traffic is uplink-only. Gateways are very good at receiving multiple messages at the same time. They can receive on 8 (or 16) channels and can decode multiple orthogonal spreading factors at the same time. This means that you can easily deploy thousands of end devices that only send uplink messages. Another assumption is that end devices only transmit very infrequently (on average once every 15-30 minutes).
For end devices, the device firmware is responsible for staying under the limit. For gateways, the backend is responsible (although some gateways also implement it in their firmware). If an end device does not comply, there probably won't be a LoRa policeman knocking at your door, but your end device will also not get the CE certification needed to sell/deploy it commercially. If a network server or operator does not comply, it's easier for the authorities to take action, so we just have to make sure to keep transmissions under the limit.