I've always had fairly neutral feelings towards the burnsteem initiative and as is customary to replying to questions, I shall ignore all of the questions and just share some thoughts. I'll probably think about it more in this reply to you than I ever have done so maybe I'll have a strong opinion by the end of it.

Once the initiative was launched, it was quickly pounced upon by the community. At the time of writing this sentence, there are 2,601 posts that have @null set as a beneficiary with a total reward of $11,507.18 - a minimum of 25% of this will get burned.

This c~$12,000 per week has been consistent for a while so 25% - $3,000 ~ 12,000 STEEM from a circulating supply of 463,270,794 STEEM = 0.0023% per week being burned. Tesco say that Every Little Helps and without being an expert on the matter, this feels very little - and to prove my lack of knowledge, the other 75% increases the circulating supply so this 0.0023% will trend towards 0. (This reminds me of my maths degree. As x tends towards 0....)

Like I say, I'm no expert.

Releasing the cynic in me - the majority of the community (bar a couple of exceptions who have discussed this well before it became an initiative) don't know (or care) what impact their burning has. They're not doing it "to increase STEEM price", they're doing it to attract sc01 votes. Obviously. And it makes sense for them to do so. 100% of $(tiny) is $(tiny). 75% of $(tiny) is $(slightly-tinier). 75% of $(boom-time) is $(boom-time). It's worth throwing those dice and hoping to strike lucky.

Repeating my comment in the last debate - it's another wasted hashtag that could be used to identify your content.

I could calculate what percentage of sc01 votes go to #burnsteem but that'll require effort on a subject that despite writing nearly 7 paragraphs on so far, I still feel nothing either way.

Circling back to @danmaruschak's comment regarding "the burn happen at the point of reward-granting", this could be more impactful as a larger quantity can be burned and there won't be a divide between "Users who feel like they're losing something" vs. those that aren't. By burning at point of distribution, nobody's losing and nobody's winning. The reward amount might be "reduced" due to the sum being burned but this would be evened out by the increase "reduced-decrease" in price from the "slower increase" in token supply. I should expand on me not being an expert to state that I don't know what I'm talking about.

So in summary, great. #burnitalldown although it's probably a bit pointless at its current scale.