I did a search of the forums and couldn't find any indication that this might have been proposed in the past - if I missed it I apologize.... but here goes.
I've never been too interested in PvP and hadn't ever given much thought to it but lately I've been reading posts in the PvP section of the forums just for the heck of it. I've noticed a lot of attention is given to PvP gear. Not being overly familiar with the ins and outs of PvP I can only assume that, from what I read, some players are much more prepared for PvP because of specific gear. This seems to be fairly common and I could see where a player might be caught completely off guard by another player who's much better equipped than they are.
So with this in mind I'd like to propose the following:
Birthday Suit PvP
In this case, by Birthday Suit I mean the clothes and wand you were equipped with when you left Ambrose's office on your very first day of wizarding. You would be allowed to use the best available spell book you have but no TC, no other gear and no pets. A set-up like this would break down a PvP match to the bare bones of skill and luck. Kind of like a W101 version of a bare-knuckles brawl. No bonus damage or defense, no added accuracy. Only your wits, your spellbook choices and the luck of the draw. Obviously matches like this would have to be limited to participant levels within certain parameters. No level 60s going against a level 20 for instance. But as long as neither combatant has received a school spell at a level higher than the opponent then all is good.
From an observers standpoint, I think this could be entertaining. And as a potential participant I think I would like to try it.
There are similar rules in some of the tourneys - I don't PvP because I'm terrible at it - but my questing group is made up of me & three excellent PvPers, two of whomare in the top 50 of the leaderboards, and one of them has participated in some tourneys with similar rules. It was really fun to watch.
Not quite as bare-bones, stripped-down as you're suggesting, but no TC, no pets. Still had gear, decks etc, but no boosts from pets or TC, and maybe no masteries, even.
But if it were just no boost clothes, spells, deck, wand, might be fun.