However, when an entire program consists of a single chain of dependent instructions, which may happen e.g. when computing certain kinds of hash functions over a file, you are doomed. There is no way to increase the performance of that program.
Even in that case, you would probably benefit from having many cores because the user is probably running other things on the same machine, or the program is running on a runtime with eg garbage collector threads etc. I’d venture it’s quite rare that the entire machine is waiting on a single sequential task!