It comes down to another simple question: Do you want your pasta to taste good?
“Salty as the sea” is one of those Italian chef cliches that refuses to disappear. But it comes from good intentions. Unless you’re specifically combating sodium in your diet, pasta water deserves a generous sprinkle of salt before you add your pasta. There’s no other way to season the pasta itself, and even with a well salted sauce, unseasoned pasta tastes bland and dull like unsalted bread, detracting from an otherwise happy pile of carbs.
When you cook dry pasta, two things happen. First, the pasta hydrates, soaking up water from the pot, dissolved salt included. Then the surface of the pasta gelatinizes, which means the surface starches burst open and form a thin membrane of starch goop around the noodle. That membrane acts as a kind of barrier that makes it harder for extra liquid to penetrate the pasta.
So if you don’t get salt inside beforehand, your pasta will never be seasoned to its core. Just don’t make your pasta water as salty as real seawater—that’s way too much, even for salt fiends.