a lot more coins are minted when silver prices are high

If you look at silver Eagle population reports, the scarcer coins are in years when silver was at about $5-9 an ounce. Nobody wanted to buy silver Eagles for their bullion value then. So comparatively few were minted, or at least a lot less than when silver prices are high and interest in silver bullion is high.

However, if you go back to the Trade dollar issue, and compare it to Morgan dollars, this argument doesn't hold up because Morgan dollars were minted whether or not the demand for them existed and supply them often exceeded demand as silver prices were low then.

So Trade dollars are rare because nobody liked them back then and alot of them got melted down. Also, they tended to be minted based on their perceived demand as the gov't didn't want to get stuck with a bunch of them in their vaults. That wasn't the case with the Morgan dollar in the 1880s. But it was during part of the 1890s.

Since few ppl collected Trade dollars, (the number of proof coins minted gives you an idea of the number of collectors), there are very few nice mint state examples around in 1873,1874 and certain mintmarks such as CC.