They aren’t reluctant to change their status, they simply can’t. Hukou upgrades only come with marriage or divine central government intervention. Even if your ancestors moved to that city a few generations ago, it won’t change your (or your descendants) hukou; ie no jus soli.
Reading about the program that was my initial guess as to how it would work as well so I was surprised when I got to this section[1] of the wikipedia article that seems to say people are deliberately choosing not to convert from rural to urban. The entire section is sourced to an article[2] titled "China's Hukou Puzzle: Why Don't Rural Migrants Want Urban Hukou*"
Interestingly, the asterisk in the title indicates the research was funded in part by the Chinese government and the user who included the paragraph/source in the article has been banned by Wikipedia[3].
Farmers do lose the rights to their land when they are given urban hukou, but that is part of the divine central government intervention I was referring to. It isn’t usually the case that they are migrants, but their land is being “liberated” by a nearby city and their hukou is being changed to urban so that they no longer have rights to that land anyways (they’ll also be given a small apartment, good luck with your new career as a non-farmer!).
This is a bit different from people moving from one place to another, and involves another nuance between urban and rural hukou within the same area.