It's true that symmetric crypto isn't entirely broken by quantum computers, although in many cases the key sizes need to be doubled. However, I wrote my original statement with that fully in mind, because symmetric crypto by itself is not really all that useful. All useful applications need at least some asymmetric crypto, even if it's just to distribute keys for more efficient symmetric crypto.

As for the alternatives to asymmetric crypto: I like lattices, I've studied them a lot myself, though not in a crypto context. But have you looked at the required key sizes of those alternative schemes? They're pretty horrible and not at all comparable to what we have today.

Obviously people will continue research on this, and perhaps something close to elliptic curves in terms of efficiency will be found. I certainly hope so, but I'm not holding my breath.

I agree that archived traffic is an issue as well, but personally I'm more worried about the future than the past.