> Processing data at the edge also makes for the best possible user experience because of the complete independence of network connectivity and hence minimal latency.

That's one particular set of trade-offs, but not necessarily the best. Eg if your network connection and server processing speed is sufficiently faster than your local processing speed, the latency would be higher for doing it locally.

Local inference can also use more battery power. And you need a more beefy device, all else being equal.