The most pernicious, hard-to-find bugs that I've come across have all been around the business logic of an application, rather than it hitting into an error state. I'm thinking of the category where you have something like "a database is currently reporting a completed transaction against a customer, but no completed purchase item, how should it be displayed on the customer recent transactions page?". Implementing something where "a thing will appear and not crash" in those cases is one thing, but making sure that it actually makes sense as a choice given all the context of everyone elses choices everywhere else in the stack is a lot harder.
Or to take a database, something along the lines of "our query planner produces a really suboptimal plan in this edge-case".
Neither of those types of problems could ever be automatically detected, because they aren't issues of the programming reaching an error state- the issue is figuring out in the first place what "correct" actually is for you application.
Maybe I'm setting the bar too high for what a "bug" is, but I guess my point is, its one thing to fantasize about having zero bugs, its another to build software in the real world. I probably still settle for 0 run time errors though to be fair. . .