Let's see if we get agreement on something:

You say toward infinity the length of a step approaches zero. Although that is correct, the sum of the length of all steps doesn't approach anything but is constant. Do you agree?

Furthermore if you look at a step as the number of steps approaches infinity you will find that the relative difference between the length of the step, as small as it may be, and the length of the line it covers, remains constant, being length of step / length of line = 7/5 (in general the slope of the line).

That is why I say it is an illusion that the steps fall into the straight line at infinity. They never do.