"There were ten dollars" sound wrong to me, because we don't call dollar bills or dollar coins (which we have) 'dollars'.
If there is a dollar coin on the table:
What is that? That is a dollar coin. Generally not That is a dollar.
If there are two dollar coins on the table:
What are they? They are two dollar coins. OR They are two coins. But generally not They are two dollars.
Actually, now that I say it a few times, "dollar" work better for a coin than it does for a note.
So, There were ten dollars on the table this morning might work better for coins than notes. And obviously, it works better for some people than others.