Like Glamador said a few posts back, all it takes is a little creativity. I think a cyborg Rider could work rather well in our day and age given the technological landscape our world has become, and it seems like a logical step they could take to re-introduce some of the older Rider concepts to a new generation. We just need a good team of writers that can take the concept and run with it.
If you look at the previous Heisei Riders we have, the cyborg concept isn't very far-fetched. Between Kiva, Faiz, Wizard, and even Agito, the idea of having Riders with these types of literal internal struggles seems to be relatively welcomed in this new era of Rider shows. A cyborg, in many ways, seems like a natural evolution of these previous ideas.
Think of it: this new Cyborg Rider could show up suddenly and mysteriously (like so many Riders before) and have the mystery of his transformation be revealed over time instead of right in the first episode. Perhaps he chose his cyborg life, or perhaps it was forced on him, or perhaps he had to in order to live. Struggling with his identity, he could explore our modern world and see how he fits into it.
I can picture a beautiful scene where he makes friends with someone similar to him that he feels empathy for only to have that person or creature be tragically killed or seriously injured ("Flowers for Algernon" comes to mind). I can picture him trying to see how different his emotions are as a cyborg, exploring different emotional experiences that normal humans go through every day (going to a theme park, taking leisurely walks, playing games, etc.). I think they could really explore what humanity actually means as an abstract concept; overall, it may be somewhat stereotypical and easy to guess by the end, but as mentioned before, a good team of writers can work with anything. Just because something has been done before doesn't mean it cannot be done well again.
As far as people with artificial limbs being offended, I'm not sure how realistic that is. Perhaps there might be a few people, but I don't know how widespread the use of cybernetics are today. I would think that seeing a hero on-screen who has a similar difficulty as you might create a sense of empathy, but having been blessed with a relatively healthy life, I cannot say how it might look to somebody with said difficulty.