I thought the same way until someone brought up this..
"It is not clear whether the nazgūl continued to wear their rings. Tolkien says both "the Nine the nazgūl keep"
[4][5] and that Sauron had gathered the Nine to himself,
[2][5] though in the latter case his meaning may be metaphorical. When the nazgūl are destroyed, no mention is made of their rings."
Sauron held the 9 as an Insurance Policy, He could control the Nazgul without the 9 Rings, but against the One Ring it would of been impossible.. Killing them by destroying their life essence contained in their Rings would be of last resort to Sauron if someone with the Strength and Will to wield the One Ring found a way to steal their Will away from his.
And Sauron did have Physical Form, it took him 1000 years after his defeat at the hands of Islidur he just lacked the Strength to wield his former power.
Even when the One Ring was destroyed Sauron survived as a Ghost unable to ever take Physical Form again, wandering the Earth as a Wraith.
Maybe a gradual increase the greater the success?
1-24 Settlements = 5%
25-39 Settlements = 50%
40-Max Settlements = 80%
Yeah, the Capture of Barad-Dur, maybe a 50-50% Chance Saruman secures the 9 Rings safety or Sauron flees with the 9 Rings to his new Capital?