ApiMain::logRequest is called after the API modules' execute actions have finished, but before calling MediaWiki::preOutputCommit. Request timings obtained that way (such as the timeSpentBackend field in ApiAction data) are not really indicative of real processing times.
That depends on what exactly you mean by "processing times". The figure currently logged reflects the time spent executing the API module, not including time spend in MediaWiki setup, API setup, or postprocessing.
Having this figure tells you that you should probably be looking at the MediaWiki setup, API setup, or postprocessing (including DB on-commit hooks) rather than the module executions themselves.
I can see how strict module execution times can be useful sometimes but I think most of the time people care about how long responding to an API request takes, and how that's split between module execution, precommit callbacks and other things is a secondary question.
"I think most of the time" is a dangerous phrase. What it really means is "this is what I want now, and I'm projecting that desire".
Nor would simply moving the timing measurement to after the preOutputCommit() call really measure "how long responding to an API request takes", because it still isn't including MediaWiki setup, API setup, output buffer writes, and so on.