Robocopy's speed depends on some options.
/Z option copies files in restart mode. When network goes down while copying, it resume next time. BUT with this option speed is not good.
/MT Creates multi-threaded copies with N threads. N must be an integer between 1 and 128. The default value for N is 8.
Since you have ~Ks of files and local network, try to use more than default 8 threads (around 25) without /Z parameter.
Also supressing file output increase speed.
robocopy source destination /MT:25 /NP /NFL /NDL
/NFL No file list - don't log file names
/NDL No directory list - don't log directory names
With these options we copy millions of files with size above 1TB, and it can utilize all 1Gbit/sec network, so the limit is your network speed as you mentioned.