I find the inverse surprising: that many algorithms that work on real-life robots _do_ _provide_ error bounds and their optimality / convergence properties are proven in the papers that introduce them.

A great example of this is motion planning, where papers both on sample-based methods (such as SST), and on search based (descendants of the A* family) argue at length the theoretical optimality and convergence properties.

On another note, I think requiring more theoretical analysis as a guarantee of safety could partially be an AI-winter meme rather than practical solution. Point in case: do people run a quick check of aerodynamics maths before boarding a flight? No - they rely mostly on the engineering and regulatory process that gradually made passenger flights safer.