This accomplishes the original goal of the initiative — to keep fixed-income seniors in their homes — without starving localities of property tax money and disincentivizing them from allowing new housing to be built.
Politically, passing these changes would still be hellishly difficult, particularly the second one, which is not so easy to understand. One way of putting the problem is that Prop. 13 represents a massive transfer of wealth from future California residents to present ones. Of course, the future ones can't vote against it since they don't live here yet.