Why are garbage collectors so important?

My take as a hobbyist in this area:

In highly complex, long running systems, it's very difficult to know automatically when memory is no longer needed.

Reference counting, and its draconian creepy uncle malloc()/free(), require programmers to be very careful about when they free memory.

This is a life of tossing in turning in bed: Did you carefully free before you returned in that error handler?

C++ has the benefit of strict compile time analysis, and a lot of the confusing bits have sensibly been pushed to the standard container types' implementations.

Dynamic systems with diverse "types" and millions of collections of objects, especially ones that are likely to contain "cycles" and references to each other, often take other approaches that aren't as "match up the alloc() and free()"-oriented, such as periodically scanning the entire object graph and deleting stuff that couldn't be reached.

Madness! But runs like hell when the graph is small and most people won't feel the burn. An ongoing area of research.

They're going for a different kind of performance. Memory safety eliminates entire classes of problems, freeing the programmer to focus on other things. For the vast majority of software projects, the performance is more than adequate, and the benefits are well worth the costs.