To "B" or not to "B", that is the question

In the recent FRED Blog post I looked at yesterday, they say

Because money is valued as a payment instrument, people are willing to hold a fraction of their wealth in money form for the sake of convenience, even though money earns relatively little interest and cash usually earns no interest at all.

I see that line of reasoning too often:

• Scott Sumner relates it to velocity: "Interest rates are the opportunity cost of holding cash.  If you lower interest rates, people will choose to hold more cash."
• David Glasner says there is "a rental price for money, and that rental price represents what you have to give up in order to hold a unit of currency in your pocket or in your bank account. What you sacrifice is the interest you pay to the one who lends you the unit of currency, or if you already own the unit of currency, it is the interest you forego by not lending that unit of currency to someone else..." He claims, bizarrely, that there is no opportunity cost if you borrowed the money you're holding, but an interest cost instead.
  

That's way more times than I ever wanted to see that reasoning.

To put it in FRED Blog terms, the "fraction of their wealth" that people are willing to hold as non-interest-bearing money changes when the interest rate changes, but in the opposite direction. Something like that.

I have a problem with this whole line of reasoning, because I'm someone who always spends money quick as I get it. I never have to decide whether my preference is to earn interest on the money or to hide the money under the mattress and "pay" the opportunity cost.

It seems to me that the understanding economists have is based on either

1. money is close enough to equally distributed that everyone has some to spare, so that everyone is faced with the question: to hoard or not to hoard? These alternatives are far more crucial than actually spending money in that world, it would seem. Or
2. money is so unequally distributed that those who have some to spare have so much of it that their decisions drive the velocity of money. The rest of us spend every dollar and have nothing at all to spare, but still don't spend enough to have an effect on the velocity of money.
   

"A" is obviously false. "B" is absurd -- it is absurd to imagine that the vast bulk of the American people spending the vast bulk of their income might have essentially no effect on the velocity of money -- and yet "B" is evidently true, as it is obviously false to say money is close enough to equally distributed that everyone has some to spare.