I absolutely can't say whether current subsidies are too high or too low or just at the right level for that purpose, but at least to a certain extent the subsidies and the resultant overproduction are intentional as a safeguard against harvest failures, because you really really don't want to end up with a famine as soon as you get an only even just marginally worse harvest.

It's the same issue we're now running into with renewable electricity production: You either need lots of storage, and for what you cannot store you need to significantly overbuild your production capacity.