I might be missing something, what makes you think there are no successor chapters? There are an incredible number of chapters with unknown founders.
Absolutely, however it is weird that apart from the Storm Giants and Black Dragons there are not even rumours about other successors. There is no info about other Chapters who have glowing eyes (which we know from Massacre is the other readily identifiable geneseed marker for the Salamanders) and for such a famous (in a good way Chapter) to have no Chapters claiming lineage from them despite 10K years passing since they were nearly annihilated.
The Raven Guard suffered horrific problems with their geneseed due to the events of Deliverance Lost and yet they were still able to produce 3 2nd founding Chapters (Raptors, Black Guard and Revilers) despite having roughly the same number of survivors after Istvaan V (around 3000).
I'm not including the Carcharodon Astra in this as technically they were of an unnamed founding which I'll call the 1.5 founding since they were expelled from the Raven Guard even prior to the Heresy and so they cannot be counted as 2nd founding (although in official records they are probably counted as such.)
We also know from Massacre that some of the Iron Hands went insane and we also know that the Iron Hands 2nd wave were also annihilated (described in Veritas Ferrum audibook) yet there were enough survivors to produce The Brazen Claw and the Red Talons at the end of the Heresy.