Should the draft be changed?

[manicmav36]

But at the same time, is it fair to the "experienced" rookie to be on the same regression as a S1 when they don't have access to the same amount of TPE that a S1 had? (Later time, training camps, etc.)

Valid point, I would say not. Your point does reinforce the argument against the obvious disparity in TPE available to players who didn't join in the middle of S1.
There would have to be some way to limit the amount of TPE earned until it is officially your rookie season. Maybe 1/2 of the usual amount awarded until then? That way you still get rewarded for your work and there isn't a big TPE advantage once regression rolls around.