I sit corrected. Instead, the current typical approach is to use cross-breeding to produce seeds that grow well the first generation and don't produce reliable seeds themselves.
That is misleading, as the goal of that cross-breeding is not to produce unreliable seeds, but in order to produce better results. Look up "hybrid vigor" for details on this. Nothing about the cross-breeding is done in order to hinder re-use of the seeds, it's just that naturally non-hybrid seeds are less effective.
As I understand it, the idea is to have two parent lines that when produce the desired traits in heterozygous offspring but not in second-generation offspring. Sort of a Mendelian DRM.
This is incorrect. As I already stated: the cross-breeding is to take advantage of hybrid vigor[1], it is not an effort to intentionally hamper successive generations. This same practice occurs in non-GMO, non-patented plant breeding, and has been done for over a hundred years[2]