Cable fence vs deck rail
While some of the reasons are likely subjective, there do seem to be some technical reasons. Looking at the RailEasy Cable Railing as an example (it was simply the first result on google), it specifies a height of 36 or 42" and post spacing of 4', both of which are smaller / shorter than is typical in a yard perimeter fence install. Fence height tends to be 6' (72"), and post spacing is roughly 6' as well, at least in my area.

The linked cable railing does indicate longer spans are possible, though it requires extra hardware to keep the cables tensioned properly. You would either need (a lot) more posts or the extra hardware, both of which increase the price and labor involved.

Taller posts are presumably possible as well, and the 3" spacing of the cables could probably be relaxed for a fence install, though the forces on the wood might become a problem. Larger spacing could also present a risk for animals or children to get their head caught.

All that said, there is a practical reason that may be why you don't see these more. Many fences are designed to provide some element of privacy. Not all fences, of course, as there are chain link, wrought iron, white picket, etc which provide little, if any, privacy. Compared to your standard 6' cedar picket fence, though, these cable fences offer no privacy because they are essentially invisible. The near-invisibility is a big selling point when installed as deck railings, as it doesn't obscure your view off the deck, but may not be so great for a fence.

Edit: Just re-read your Question and realized you were talking about replacing a front-yard fence, so the above may not be entirely applicable. Front-yard fences tend to be shorter, so a 36" fence may be more appropriate, and you may not be looking for full privacy. Some of the other issues still pertain, and in this case, it may be down to aesthetics - from afar, a cable fence would look like a bunch of wooden posts stuck in the ground, which is probably a bit weird for your neighbors. The cables would only become visible as you drew closer.