+1. Agreed.The paradox of continuity...
To have or not to have...
Exhibit A.
Without a sense of continuity, every story would have to involve the origin of the characters, since any origin mentioned before would be wiped clean. Unless there was continuity.
Exhibit B.
Every character would have to be introduced to every other non-regular cast member. Unless there was continuity, how would you explain that character A has already met character B?
Exhibit C.
Some genre conventions rely on continuity. Take for instance vampires. While not all vampires are the same, the limitations, weaknesses and habits have to be explained to the reader to give them definition. Without continuity, you wouldn't know that this specific type of vampire is immune to sunlight unless you mention it in-story. Which brings us to...
Exhibit D.
Exposition. Long out-of-favor and now considered old-fashioned or "old school", exposition will rear it's head up because you will have to explain Everything to the reader in Every issue. Unless you have continuity.