I don't know when this happened exactly, but some time last year after this thread was created, I believe, the DCI answered the questions in the OP.
The official Banned and Restricted List page now contains a statement of purpose:
"One key to the continued health of Magic is diversity. It is vitally important to ensure that there are multiple competitive decks for the tournament player to choose from. Why? If there were only a single viable deck to play, tournaments would quickly stagnate as players were forced to either play that deck or a deck built specifically to beat it. In addition, different players enjoy playing different types of decks. If there are plenty of viable options to play, there will be more players at more tournaments. To help maintain the diversity and health of the Magic tournament environment, a system of banned and restricted lists has been developed."
Not incidentally, that is essentially what I said in this thread:
@smmenen said in Why do you think we have a restricted list?:
I answered that question, from my perspective, here: http://www.eternalcentral.com/so-many-insane-plays-suggested-banned-and-restricted-list-updates-2018/
The main purpose of the restricted list, in my view, exists to maintain and promote competitive balance. The DCI is basically analogous to the FTC or the Justice Department vis-a-vis the market. The Restricted List is the regulatory mechanism, and the DCI is the regulatory body that manages that mechanism.
The restricted list also exists to ensure that the format is sufficiently interactive (or even better, that there is sufficient "counter play."
It accomplishes both goals by 1) regulating dominant strategies, both monopolies and oligopolies, and 2) ensuring there is enough counterplay by regulating decks that win too quickly or shut out an opponent from doing anything, like Trinisphere or Flash.
The reason that Vintage has a restricted list instead of just a banned list is so that there is an official, sanctioned format where Magic players can play all of their cards (to the maximum extent possible).
Also, a corollary to that is: What do you think are the criteria R & D uses to decide what is on the restricted list?
The DCI manages the Vintage restricted list, not R&D. R&D is the team of staff that designs and develops new cards.
But assuming you mean the DCI, they provide public explanations, so you can parse their explanations for Vintage. I have done so as part of my History of Vintage Series, and found that the DCI's bases for restriction have evolved over the decades of Type I and Vintage player, and is not entirely consistent or internally coherent. They have evolved just as the game has.
But, by and large, the grounds they offer in their explanations for restriction and unrestriction generally match those I articulated above.
Also, that statement of purpose bolsters the argument I have long made, that any restriction that is taken for reasons other than promoting format diversity, such as "play pattern concerns," would quite obviously have the potential to undermine the 'diversity' of the format, and therefore undermine the main purpose of Banned and Restricted Lists.
So, for example, restricting Paradoxical Outcome would quite obviously remove that deck from the format. Unless you could show that restricting PO would open more deck options into the format than restricting it would take away, such a restriction would harm the central purpose for which the DCI states it has created B&R lists in the first place.