Why are only Homo Sapiens left?

We currently don't know what erased the other hominid species and many of the original theories are starting to be proven false. We assumed that Neanderthals were made extinct due to climate change, but that was recently disproven by Universita di Bologna.

"The analyses we carried out show little variation in rainfall between 50,000 and 27,000 years ago, the extent of this variation is not enough to cause alterations in the flora inhabiting the environment above the cave. Carbon isotopes show that the bio-productivity of the soil remained all in all consistent during this period that includes the 3,000 years-long coexistence between Sapiens and Neanderthals. This means that significant changes in flora and thus in climate did not happen." -Researcher Jo De Waele

One more recent theory is the technology hypothesis:

"According to this hypothesis, the Homo Sapiens hunted using a technology that was far more advanced than Neanderthals," and this represented a primary reason to Sapiens' supremacy over Neanderthals, that eventually became extinct after 3,000 years of co-existence." -paleontologist Stefano Benazzi

So, they might have been eliminated by us homo sapiens or inbreeding or both. It might lean towards the first option since recent evidence shows H. sapiens may have been at war with Neanderthals for over 100,000 years.

The book "Sapiens" by Yuval Noah Harari takes a look at multiple reasons. One can be genocide by Homo Sapiens, since they could compete for teritory and because they were different, genocides happened between Homo Sapiens too, so we are not the most tolerant race. Interbreeding is also possible, or a mix of extermination and interbreeding There might be the case that some humans in different areas of the world have more DNA from the other species, but scientis consider this theory Pandora's box since we know how people treat skin colour different, so you can imagine how lther species would be treated.

Disclaimer: That is my understanding of the stuff explained in the book.

You have answered your question here:

DNA evidence shows that all of these groups interbreed with the other groups.

Thus it is not that these other hominin groups became extinct - their DNA lives on in modern humans - but that most of their DNA heritage has evolved out of the modern line by virtue of being selected against.

Modern humans are the descendants of all of these lines. Over 90% of our DNA is identical to the other great apes. Another few percent is from the those other hominim groups that preceded Cro-Magnon man out of Africa. The remainder, a small percentage of our total DNA lineage, is uniquely inherited from the Cro-Magnon lineage.

We - modern man - are mongrels and hybrids who have benefited by possessing the DNA of all our ancestors.