It was ~0.2% of the US vehicle fleet. Whatever sense it did or did not make, it seems pretty unlikely that it is having any significant effect on the availability of cars 10 years later.

(yes 2 tenths of a percent, 2 vehicles out of 1000)

Believe it or not, the used car market changed drastically. I regularly shop around for cheap beater cars to fix up. Before the program, there was never a problem finding a running car for $500. It was also easier to find used parts, as cars would go through a part out process before recycling. The program required the cars to be crushed with no hope of salvaging good parts from them.

~700,000 cars were crushed.

~170,000,000 new cars have been sold in the meantime (so assume tens of millions of used car transactions related to that).

It was a blip. It's more likely that other factors are driving the change in the market.