I know that several if not most top-series NASCAR teams use tungsten for ballast in their race car frames and some still use lead. With what they're spending to go racing for dollars, what's a few hundred bucks for some tungsten ballast weights if it helps them if even only a little?
Latest spot price for Tungsten is about $2,000 per
ounce - significantly more than gold - so you're not talking "a few hundred bucks" for tungsten ballast. Especially since NASCAR ballast is usually measured in tens (or even hundreds) of pounds. In other words, even the best funded NASCAR teams would be hard pressed to justify tungsten as simple ballast. Tungsten is however very, very strong so it's use can be justified for other reasons.
Back when I was still racing, the trick set-up in one class was to use tungsten weights in the clutch - it allowed the use of stronger springs for better clutch engagement. A clutch set of tungsten clutch weights - less than an ounce of the stuff - cost more than the clutch itself...
I wasn't able to find anything meaningful on the cost of DU, but since it is basically a byproduct with limited commercial usage I suspect it is relatively inexpensive.