On the topic of why there are many branches in the Balkans, several options present themselves:
a) it's the primary radiation point for PIE
b) it's a secondary radiation point for a PIE that originated elsewhere
c) it's a refuge area: there used to be many more PIE branches but most have been steamrollered by later migrations - specifically, by Celtic and Iranian, two highly aggressive cultures that came to dominate vast areas. As a result, in those areas the other branches didn't survive long enough to be attested. For instance, Howl mentions Iranian dominating the steppe. OK. But there's no evidence of Iranian (which probably originated near the Caspian in Sintashta) anywhere on the western steppe until the Scythian migration. Before that, the area was dominated by the Cimmerians - what did they speak? Clearly Indo-European, but the handful of attested names can't be definitively shown to be Iranian (and as they're the names of late-era ruler after the Scythian invasions, they may not be native Cimmerian anyway). Maybe Cimmerian was in its own branch - we'll never know. Now, some ancient sources suggest a connection between the Cimmerians and the Thracians - but Thracian survived to be attested, and Cimmerian (basically) didn't. So Thracian looks like a branch, and Cimmerian gets forgotten. Likewise, virtually no hint of any of the PIE languages of western europe before Celtic has survived (except maybe Lusitanian in Iberia). And absolutely no hint of the PIE languages spoken in Siberia!
d) the Balkans were a relatively advanced (so there's some writing) area adjacent to Greek and Roman civilisation (so there's lot of archaeology, and some ancient references and descriptions). Is it a great surprise that languages adjacent to Greece and Rome got attested when others didn't?
But the river tripped on her by and by, lapping
as though her heart was brook: Why, why, why! Weh, O weh
I'se so silly to be flowing but I no canna stay!