You don't say "may" till third paragraph.
Horse-drawn wagons and chariots are tools, not people.
Human bodies are tools as well.
If augments are invented in the free market capitalist way humanity has been doing since, like, forever, it's going to be costly at first. This means even if the writing is on the wall that it's in everybody's interest to get augmented, the shift will be gradual, which goes back to my point that people will still recognize each other as "human".
So what? So let's say it takes a century to get those costs down to the point where such augmentations are affordable for the average person. You still have 900 years left.
What is the practical and economical reason that humans abandon their old forms for a new non-human form? This implicitly assumes that this is a more economical solution than developing a tool to take on those non-human characteristics.
Because the new forms are better, practically and economically. The killer app here is health. If you have a body and mind that can last thousands of years, then that's a huge advantage over the current human body. And while the human body and mind aren't bad as tools, we probably can do a lot better than that in terms of pushing physical and mental limits, or in interfacing with our other tools.