I have heard that it was suboptimal for C to automatically collect garbage — is there any truth to this?
Was there a specific reason garbage collection was not implemented for C?
Don't listen to the "C is old and that's why it doesn't have GC" folks. There are fundamental problems with GC that cannot be overcome which make it incompatible with C.
The biggest problem is that accurate garbage collection requires the ability to scan memory and identify any pointers encountered. Some higher level languages limit integers not to use all the bits available, so that high bits can be used to distinguish object references from integers. Such languages may then store strings (which could contain arbitrary octet sequences) in a special string zone where they can't be confused with pointers, and all is well. A C implementation, however, cannot do this because bytes, larger integers, pointers, and everything else can be stored together in structures, unions, or as part of chunks returned by malloc.
What if you throw away the accuracy requirement and decide you're okay with a few objects never getting freed because some non-pointer data in the program has the same bit pattern as these objects' addresses? Now suppose your program receives data from the outside world (network/files/etc.). I claim I can make your program leak an arbitrary amount of memory, and eventually run out of memory, as long as I can guess enough pointers and emulate them in the strings I feed your program. This gets a lot easier if you apply De Bruijn Sequences.
Aside from that, garbage collection is just plain slow. You can find hundreds of academics who like to claim otherwise, but that won't change the reality. The performance issues of GC can be broken down into 3 main categories:
The people who will claim GC is fast these days are simply comparing it to the wrong thing: poorly written C and C++ programs which allocate and free thousands or millions of objects per second. Yes, these will also be slow, but at least predictably slow in a way you can measure and fix if necessary. A well-written C program will spend so little time in malloc/free that the overhead is not even measurable.