How many states do you imagine would have "signed on" to the union knowing that they were to become "mere administrative regions"?
None. I am not claiming the Consitution provided for such a lowly state for the states. That would be well, errant.
Most, it being a question of the big states having more authority than they should and the little states being squeezed out but going along because they have to eventually. Would the borders of the admin regions be adjusted to even out population numbers? That would end up the same as squeezing out the little states, too. Opinion was split at the Constitutional convention just as it is here. The FedGov ended up with either too much power or not enough power depending on the state in question, and we're still right there after all this history.