Average time would indeed be a better description. 

As for its usefulness: let's say that for example you would want to find the function in which your code spends the most time on average, in order to later optimise said function. If one of the calls to another function has its execution time spike momentarily, it will be at the top of the total time column on the result. However, that does not necessarily mean that it was the function in which on average the most time was spent on, and thus the one that the optimisation effort should be focused on.
Also, when seeing the profiling results, I would expect to be able to sort by any of the columns shown, and that is currently not possible for the average cumulative and total time per call.

Do you mind clarifying your worries with backwards compatibility? Unless I'm mistaken, "fcn_list "is the only outside effect of the method I'm changing. It is built from the last element of each tuple in stats_list, whose ordering is what I'm proposing to be able to change (thus changing the ordering of the function list, but that is already done by other sort options).