Nope. This is a misconception.

Batteries don't have rare-earth materials in them. Lithium, nickel, and iron are very plentiful in the US. The "rarest" of materials that might be mined is Cobalt. That, however isn't because it's a hard to find. Rather, cobalt has basically no industrial applications outside of battery production. And, importantly, not all battery chemistries require cobalt, just the nickel manganese cobalt batteries.

Idaho has a cobalt mine that's not currently in operation. The reason is because demand is super low and the artisanal mines in africa are cheaper than spinning up a full industrial mine.