That metaphor doesn't work for two reasons. First, over time a car has grown MORE complex, while the tools to create a website have grown LESS complex. At the same time, improved quality in engines, motor oil, and service technology has made routine maintenance not only easier, but also less expensive. Second, auto repair, like most skilled trades, is a great example where specialization of workers gets involved. It's not that you can't spend the time to learn how to repair a car, it's that you consider your time worth more. But in many cases, the cost of building a website has come down so rapidly that it doesn't require a big time commitment for many people.
There will always be room at the high end to solve problems that are complicated, large, or rare. But at the low end, things that were new 20 years ago just aren't anymore. Website development is becoming less like a mechanic and more like pumping gas.