I would consider that any driver who's following all the rules of the road and posted signs (which would and should be different for these small, narrow side streets) should be freely able to use that road if it gets them where they want to be faster or more conveniently, and that them using these streets in that way should NOT be considered abuse.

If there's a mismatch between the planners' intent and the posted street signs, speed limits, etc - that's a fault of the plan and the planner's; street signs delineating how drivers should behave on these streets are a key part (if not the main part) of city traffic planning. Drivers have to obey the signs, and they don't have to obey some official's intent - so if some streets have lower speed limits or speed bumps because they're residental areas, then that's completely fine and both drivers and Waze will take that into account when routing.

But in general, if it's a public street, then the public (including nonlocal public!) is meant to be there if they want to; if it's not a private street of a gated neighbourhood then the drivers passing through have the exact same right to use that public street as the people who live there. It's not at the expense of the people who live there, it's simply using your own rightly deserved share of that public street instead of expecting that those other people have a monopoly on it and that you'd need their permission to share that street with you - if anything, you could label the desire to keep others off "their" street as doing so "at the expense" of these other taxpayers. You can plan and build non-arterial streets so that they're more useful for reaching local stuff and less useful for passing through; however, if the locals are allowed to drive through that street with x mph, then arbitrary numbers of other people are (and should!) also be allowed to be there on the same conditions.