The "cliffhanger" denies the premise of this question and is the in-universe explanation why destroying Genisys does not have a large effect.
The 'bad writing' could just be that our protagonists do not understand very well how modern computer software is deployed. They thought it would work, so that became their objective.
Why they thought that is the real question - but it's a moot one, as that's not in the script.
Out-of-universe, the author realized that you don't end a franchise that could later net you millions of dollars. There's an alternate ending for T2 which was filmed, but was not included in the release, because it brought the entire story to an end.
The "problem" with the first two James Cameron-directed Terminator films is that they were satisfying. They told a complete story and left the viewer with the distinct sense that the tale had ended, though the final moments in Terminator 2 included the visual of a dark road with a note that no one knew what the future would hold.
–Terminator 2's original ending would have made the sequels impossible, polygon.com
As opposed to the deleted scene where grandma Sarah sits on a park bench watching John push his child on a swing.
August 29th 1997 came and went. Nothing much
happened. Michael Jackson turned forty. There
was no Judgment Day. People went to work as
they always do, laughed, complained, watched
TV, made love.
–T2: Alternate Ending, killermovies.com
Not including the cliffhanger in Genisys would have been the same mistake of including that scene in T2. Not that it was really necessary, given that most people understand what The Cloud is and how it works.
So, somewhere during the post production of T2 it was decided that, no matter how much the ending of a story might invalidate its plot,
awful writing it must leave room for the search for more money.