With the convert button the SBD holder is guaranteed a dollar from the Steem blockchain
No! The converter is guaranteed to receive a dollar in expectation (more or less). In practice it will be more or less than a dollar, depending on the fluctuations in the STEEM price between the time the conversion is requested and the time the STEEM is delivered.
Now I know many people do like to play the lottery, but in practice I very much doubt that the typical user of Steem is ever served by using that function and receiving some unpredictable amount of STEEM more or less than one dollar. It is part of the mechanism yes, but it can (and should) be left to sophisticated users and traders who can access it via other means such as the blockchain (cli) tools, vessel, etc.
I'm pretty sure that at last 90% of the time when the 'convert' function in the UI is used, the person doing it does not understand how it actually works, what they will receive, and how it is determined. Needless to say I agree with @biophil about removing it from the standard UI, or at a minimum hiding it in an advanced section.
Do you know a any source material that describes the how this works? I have read the white paper. Which tends to be a bit vague at points. Also, I've been supplementing this reading with people's interpretations of the white paper and other sources or sadly, maybe just what they made up. After digesting this information and disregarding much of what I read, I came up with what I thought was a coherent system.
My understanding of when the rate was determined was at the end of the 3.5 day period, not as you stated, over the whole period (my interpretation, please correct I am wrong). I have read that the purpose of the waiting period was to prevent gaming the market by large transactions of Steem and benefiting by a coordinated conversion of SBD. So if what you are saying is that the rate is the average over the waiting period, then it makes sense that disrupting a market for the whole 3.5 day period is harder than just at one point. Again, 'taking the average' is just my hypothesis. One that needs tested. Unless you can shed some light on this?
Anyway, this is the sort of logic I've been using to deduce the working of this ecosystem. I wanted to test this hypothesis but I still have not found where the conversion rate is published. Although, I was able to find out that it is the median value set by the elected 'witnesses'.
So, in conclusion I think I will go back and reread the white paper and if anyone can point me to any other official documentation describing this system, I would love to read it as well. Also, thanks @smooth for pointing out where I need to focus to clarify my understanding.
BTW, I still feel that if you hide the convert button, people will not even know that it exists and that will slow down their learning of how this system works by giving them a false sense that they already know everything. When in fact there are whole functions that are available to them with out them even knowing that these functions exist. That has always been the problem with CLIs. At least with a menu you can see the functions that exist and do some reading about them in some what of a random access order. With a CLI you have to start from the beginning of the manual and read to the end or at least until you find what you need. Of course, there are indexes to help but people will not look to an index without a prompt that a function exists.
Every hour the blockchain takes the median of the witness price feed inputs. After 3.5 days, it takes the median of those hourly samples (over the entire 3.5 day period).
So, yes it is more difficult to disrupt the price over that entire period, but the resulting payment may be more or less than $1.
Unfortunately the state of documentation on the Steem platform is not the greatest and there have been many rounds of changes and adjustments, not all reflected in documents, which in any case are often not complete. Unless you can work it out from the code itself, often the only way to find out how the system works is to ask someone who is familiar with the history and current rule set. Not an ideal answer, but it is the best I can offer.