My understanding from the episode is that the plan was never for the public lands to grow in value. The private lands were given away or sold as incentives, and the owners could choose to capitalize off them immediately (e.g. as soon as the railroad reached nearby) or hold onto them for profit.

But this is verbatim what the article saud, you should have read it: "This checkerboard pattern allowed the government to keep all the undeveloped sections in between and wait for them to go up in value before turning around and selling them to developers."