Haven't really used the Javascript debugger, but my guess would be completely infeasible to follow everything a random "modern" Web site might do. And as you say some Javascript might be compressed or obfuscated. What I really would want is a somewhat higher level / more filtered approach: Like strace lets me just trace file operations for example.
Additionally, you can set breakpoints on event handlers and Chromium has deobfuscation built in. You can usually tell approximately what's going on by stepping through the code and watching the variables in local scope.
Right, so you are describing the implementation of the tool I was looking for. Obviously I don't want to do that manually while tracing a page.