I don’t have a good answer, as (surprisingly) I have not paid close attention to the genesis of Koine. But let’s separate out the various things that happened, and that other respondents have highlighted.
Eleftherios V. Tserkezis correctly highlights that the koine was a dialect koine before it was anything else. And the dialect koine did what he said: given several options, it would pick the most consistent or easiest to learn.
1. Phonetic simplification. Arguably underway in some dialects before Koine—Boeotian I think came up with some iotacism way before, for example. The phonetic simplifications were natural trends, of the kinds that Steve Rapaport investigates. Any tendency to simplify the phonemes foreigners had to learn was welcome; but that tendency was likelier to prevail if it was already underway in at least some speakers. So iotacism was likely already underway, and the foreign language learners may have just encouraged it.
The typologically more commonplace changes, like fricatives for aspirates, may have been more a foreigner thing, or just a natural thing nothing to do with Koineisation. The vowel meltdown seems to have been quick; the consonant meltdown was not.
2. Morphological simplification. Here the role of dialect was important, because different dialects offered different options, which foreigners would not have just invented. Hence the abandonment of Attic peculiarities (and they really were peculiar), such as the Attic declension -εώς in favour of Doric -αός, or of -ις -εως in favour of the Ionic -ις -ιος. (Surprised by that? -ις -εως came back in learnèd Greek.)
So foreigners mattered, and there’s a parallel for that kind of scenario in what happened to Old English when the Vikings came to town—the differences in inflection were smoothed over.
But more critical was the increased mobility of Greeks of different dialect backgrounds, outside the city states, and without clear dominance of one group over the other. Ok, the basis was still Attic, but it was an Attic that could pick Ionic and Doric alternatives when they were easier. The dialects only died out around the first century AD.
There’s one parallel in Modern Greek to koineisation: what happened in Athens in the 19th century. The basis is Peloponnesian, but there’s other bits, which randomly came in via prestige (Constantinopolitan, we suspect, for the northern Greek -οῦσα imperfect, and the Northern accusative indirect objects could have been adopted as well); and if a dialect happened to resemble Puristic Greek, its form was boosted (there’s some Heptanesian forms in the standard—I forget which—which are better explained by their similarity to Puristic).
There’s another parallel in Modern Greek, to “contact with non-Greek speaking people”, which is a lot closer to the Koine story, though less well studied. In fact the only statement of it was a throwaway line in paper by Richard MacGillivray Dawkins in… 1940?
Islander Greek and Mainland Greek are different. Islander Greek is more uneven, has more archaisms, has more exceptions all round. Mainland Greek has a smoother, simpler grammar.
There was lots more use of Greek as a second language on the mainland.
Which sounds like another discussion we’ve been having, Dimitra Triantafyllidou.