> Modern sailing vessels always sail into the wind, because they're always going faster than the wind blows.

Maybe state of the art hydrofoiling boats, cats and some quite large monohulls, but maybe that's what you meant by modern. Most sailboats built today have a pretty low top speed (due to hull speed limitations) relative to wind speed - monohulls often max out around 5-6 kts aren't going to be faster than the wind pretty much ever