And my question is what industries that don't have competition also don't innovate? I am not aware of nor can play devils advocate and try to imagine an example.

Had deregulation not happened for airlines in the 70's, why would we expect that they wouldn't innovate to produce less expensive and more reliable aircraft? Any sort of improvements there makes a bigger profit and avoids killing customers (also pretty good for profit).

There are plenty of examples. I will give one in transport, as we are discussing here.

Seoul and Tokyo have the most extensive subway systems in the world. Both have both privately owned and de facto government-owned lines through government business entity. The innovation here is connecting key areas in the city. The new lines that connect new city centers that emerged are privately owned; they care about profit and they are incentivized to provide popular, convenient services by connecting new city centers. Also, there are other innovations like self-driving trains in those private lines (see Shinbundang Line, the newest in Seoul). A government line with legally guaranteed profit is less poised to innovate although some innovations happen due to popular demands or government initiatives.

It's not that government-led projects have zero innovations, but they tend to have less momentum than well-motivated well-aligned private corporations. Well-aligned (with the public's interest) is the key here.

I don't know if particular examples prove anything, but you asked for examples, and here it is. We do have decades of economic research that competition generally leads to innovation in services and technology.

Regulatory capture is far more profitable than innovation.