I have only done this once, in my own backyard, but I am also in the business of aesthetics, so I thought I would chime in. In my situation we went with option #2.
I would not recommend option #3, due to purely aesthetic reasons, unless you would like to keep the fence low all the way down for some reason (light, neighbors wishes, view). Having the gate suddenly jump up by 4' at the end would be quite strange looking, in my opinion.
If you go with option #2 the fence will be high in the back corner, which will allow for taller plants and more landscaping options, and will just look better in general. You get the same effect with option #1, however, it is more of a pain to do all the cuts necessary to slope the bottom, which after a little bit of growth from the landscaping you will never see. It would really be a pointless detail. In my experience, once we got building we were very happy that we had decided against doing that very thing- it's enough work already! And after just a couple months of growth the bottom of the fence was totally obscured anyway.
I wonder if your house is a mid century style? Horizontal fences always look great with this style of house- I also prefer them over vertical for almost everything. I wish I could send you a pic, but I don't live in the house anymore and am renting it out. Anyway, I hope my two cents helps you decide!
Best Answer
Is there a reason that this style of fence is not suitable for a yard perimeter?
I can think of a few reasons why people might think they're unsuitable for their front yard. But I don't see why you couldn't do a cable fence if that is what you like.
Pets
Often, the reason for fencing a front yard is to create a barrier so small dogs and toddlers can run freely without ending up in the middle of nearby roads. Chain link and picket fences do a fine job of this for a reasonable price, they are readily available in a wide variety of styles at mainstream hardware stores, so they are an easy go-to option. Cable fences on the other hand would be easy for an unsupervized dog or child to squeeze underneath or through.
Aesthetics / status symbol
The fence selected is often a small part of the owner's overall landscape "vision", or at least they have put some thought into what it looks like and how that look complements the rest of the yard/house. As mmathis said - you don't really see the cables from a distance, only the posts, which might seem odd.
It's not trending in suburbia / looks too commercial
Most of the times you encounter cable fences will be on tall buildings, cliffs, harbor walls, shopping mall balconies, etc., where the primary purpose is to prevent people from accidentally falling off an edge while at the same time not spoiling the view. It may simply be that people have decided that's all they are really meant for and just never considered using one for a private installation.
Complexity
After sinking the posts, the other fence options don't require any specialized knowledge or skill (E.g. tensioning cables appropriately), you just attach everything with bolts. The other options are just easier.
Cost
There are cheaper alternatives.