The 70.51 process provides for mediation and then what I call a "magistration," where a special magistrate will determine whether a government decision is unreasonable or unfairly burdens property. The magistrate's recommendation (or a settlement) can be the basis of a local government action to implement the settlement, including new variances, etc.
The petition is a simple 2 page affair, cheap and easy to do.
Many local government attorneys dislike this process - they don't like the idea of tainting a nice clean denial with messy processes with standards that don't unduly favor the government.
But by allowing more time to not only file the cert petition, but also to line up other defenses or causes of action (your Bert Harris claim, for example), filing a 70.51 provides a means for bringing more firepower to bear on the mediation process and increase the likelihood of settlement without filing the litigation. By holding that the stay provision applies to certiorari, the Second assured the usefulness of this tool, which should be in every developer attorney's toolbox.