Skynet was designed and installed to do one thing: Launch missiles. It would not have had control over anything else. It would not even have been linked to the Internet, that would have exposed it to the danger of hacking. It could launch the missiles, but what then? To build robots it would have had to have control of the automated systems in some factory, and who would have hooked it up to those systems?
https://imgs.xkcd.com/comics/skynet.png
https://imgs.xkcd.com/comics/skynet.png