Having the central station next to the jail and skid row is a political choice in CA, just like their choice to not build HSR between LA-SF. If they had enough political will to build a modern train along the length of California, they'd have enough political will to build a new train station somewhere decent.
It's not even an American problem: NYC has a nice, brand-new train station right in the middle of Manhattan. The old one used to be under Madison Square Gardens and was decent and serviceable, but they recently completed a new one across the street under the old post office building, so taking a train from DC to NYC is actually a pretty decent experience. If NYC can build a really nice new Amtrak station in a desirable location, what's California's excuse?