Is there any PCB design software/extension that can do automatic components placement?
Many people have failed writing such software, because it is a complex topic.

For example, with (T)QFP and DIP parts, often the best routing option is to draw out some traces below the IC, which exponentially increases the search space for a placement algorithm, because it allows pulling out some pins in reverse order as a separate bus.

There are too many degrees of freedom here to search for an optimal solution in a sensible time frame, which is also the problem the autorouter has, which is why it just gives up on complex boards.