Really, SBD is a redemption certificate. To be redeemable, there has to be some guarantee that it can be redeemed (converting is redemption, basically).

It doesn't matter how much people want them, or want to get rid of them, the price cannot widely diverge from USD. The difference between the two is paid for by every holder of steem because when SBD goes up, steem supply has to be increased, which devalues the Steem (demand high). When the demand for SBD is too low, it's not such a bad thing - this causes contraction of Steem supply - but this can have a downside too because it reduces the amount of Steem that can be paid in post/curation rewards, in the short term.

Thus, the more SBD there is, the more likely the supply of Steem is going to rapidly change, and this leads to a situation where the supply of Steem has to be continuously increased over time to hold the peg. This causes an asymmetric pressure on the Steem price, specifically, downwards. If the SBD goes down in value, steem supply has to be contracted, and if this were to go on for a long time it would reduce the amount of steem distributed to post rewards (and possibly witness payments too), though the contraction of supply would then cause a bounce in the price, which would then drive up the SBD.

The big spike in SBD was caused by this, I believe. Have a look at the chart to see when the steem price went up to nearly $0.40, and then a delay, and SBD went up in value sharply. I am not sure exactly what the delay was but I suspect it was almost exactly a week, or two weeks, which is a period during which supply parameters for both are calculated.

Also, regarding interest paid on SBD, I think this is wrong. Interest payments are supposed to be the compensation for not being able to spend it today. You can spend this asset. Although banks do issue somewhere around 1-2% interest on cash deposits, this can only be sustained in a bull market. If these interest payments on spendable liquid assets rise, while the economy shrinks, everyone is heading for the poor house. Being paid to spend money is getting your cake and eating it.

There is so many proverbs about this, that I am amazed anyone thinks it is ok to pay interest on liquid assets. Just because they do it in the banking system does not validate it.

A bird in the hand is worth two in the bush

You can't have your cake and eat it too

If I lend you money, I should get more money back in return, because I was unable to spend it during that time. This interest rate is supposed to be regulated by how much money is being held off the market. Lots of savings means low interest rates because the supply of lendable money is high. When nobody is saving, the interest rate has to go up because otherwise people will consume more they would, consumption is the destruction of wealth.