I actually don't have a huge problem with the deliberately archaic English in certain games - admittedly, the cod-Shakespearean dialogue isn't the greatest in games like Vagrant Story or FF12, but I can deal if it's something medieval-y in setting. (Since actual medieval English would probably be a bit difficult for modern audiences.)

However, it definitely can get kind of annoying when they go over the top with it (mostly because they tend to use a five-syllable world when a one-syllable word will do, like VS' repeated use of the word "escutcheon" over "shield"), and they tend to do so a lot. I much prefer a mix of casualness and formality, along the lines of Dragon Age (which had fantastic writing, albeit originating in English).