Shakespeare is modern English; even Chaucer, ancient as he seems to us, wrote in middle English, I think.
Absolutely correct. There are three primary phases of English: Old English, as found in Beowulf; middle English, as in Chaucer; and modern English, of which Shakespeare is most definitely an example according to any history of linguistics.
As for Steve's example, well, yes, there are defective lines and other textual problems in the various sources. But there's a major difference between scholarly editing to reconstruct the most probable syntax and meaning of various lines, and modern "updating" to substitute 20th-century vernacular for Shakespeare's own language.
Steve claims he has read the "folios." Good for him. All four editions of the folio from 1623, 1632, 1663, and 1685? Has he read all the extant quartos as well, including all the so-called "bad quartos"? Does he know which plays have only been transmitted from the First Folio, and does he have an opinion on (say) the textual problems of King Lear, in which there are significant discrepancies between the first quarto and first folio? Does he think in such a case that readers should use only one or the other version, or would he follow Alexander Pope's lead and conflate the two to produce the most complete text based on the available source material?