I can't entirely agree that this would be a fair system.
From a laymans points of view one day one group of 1000 people may burn 1 btc each and the next only day a group of 100. If 1000 NEX were released both days, one day they all get 1 NEX the next they get 10 NEX. This hardly seems fair to the first group to reward the second group 10x the amount based on random chance.
What would happen in this scenario is people would watch the burn address to know how much NEX they would get out on any given day. This might make it more profitable to just buy the NEX from someone else if the daily burn was oversaturated (that is, the amount of NEX you could receive from the burn would be less than taking that BTC and exchanging it for NEX directly).
In this case, the price of NEX would be tied to the amount of NEX you could get from the burn on any given day, or vice versa, the amount that people would/could burn would be directly tied to the price (would it be profitable to burn X amount of BTC if I'm going to receive Y NEX?)
It seems like instead of being used for people to adopt NEX, this burn/faucet would be monopolized by bots whose soul purpose was to eek out small profits whenever they could get more NEX by burning during a burn period than by buying on the exchanges.
In fact, no one would burn except within the last minutes/seconds of a burn period so as not to dilute the share of NEX dispensed (why burn when you don't know how many others are going to burn and at what amounts? It might be more profitable to buy off an exchange)
What am I arguing about? I don't know. But someone has to.
In all respect, but from what I read it seems you still haven't understood my proposal. You are talking about "last minutes/seconds of a burn period" but what I propose is a sliding window, so there is no end of any burning period!
Furthermore, in your argument you somehow make the assumption that the free market to decide if burning is profitable will not work. If your argument would be valid, then the whole bitcoin mining would make no sense, because free market decides if your energy costs are worth to mine bitcoins. So the decision to mine Bitcoins or not to mine Bitcoins depends obviously on the exchange rates in the following loop:
BTC(exchanged) <-> USD -> proof-of-work-energy-cost -> BTC(mined)
A miner can calculate his rewards and the free market will decide if it is more profitable to go the route via exchanges or to mine.
My proposed system actually completely rebuilds this free market reward system:
NEX(exchanged) <-> BTC -> proof-of-burn-btc-cost -> NEX(mined)