2 post lift install -- documented

So I know nothing about lifts, but I see people doing what you do a lot to install them. My question is, why not just remove the piece of concrete between the feet pads? Like a big rectangle of concrete so the new thicker part is the entire width instead of just under the lift feet? Wouldn't that also be stronger with less likelihood to shift in relation to the old slab?

Either way, nice work, my garage would have everything coated in concrete dust if I were to do that job!