It’s very hard to know. Language change is a bunch of stuff that happens, and language does not always change in an optimal direction. Greek has certainly retained its equivalent words, proxtes and methavrio (and even one more day out: antiproxtes, antimethavrio), it’s not like the concept had become suddenly useless.

The following is necessarily speculative. And these would be necessary but not sufficient conditions for the change.

The formations were no longer semantically transparent, and sounded archaic. Ere and morrow were obsolete. Over meaning day after was likely a dead metaphor.

and were obsolete. meaning was likely a dead metaphor. The formations were useful, but not essential. So they did not have to be replaced when they dropped out of usage. We had days of the week, and we had calendar dates.

More speculatively: as a highly literate society, the early modern English were more across what day of the week and date it was, than their mediaeval English counterparts, or their Greek contemporaries. If you are a peasant and don’t regularly go to church, why would you need to know what day of the week it is? I know I have no idea what day of the week it is, when I’m on holiday.

EDIT: Vote #1 Brian Collins: Brian Collins’ answer to Why have the words “overmorrow” and “ereyesterday” gone? Was it easier for speakers to use “the day after tomorrow” instead of “overmorrow”? OED tentatively agrees with him that overmorrow, ereyesterday were made up by Myles Coverdale. (See my comment there.)