My understanding is that they compete within the states where they do business, but pools, premiums, etc., are calculated down to zip code precision. That is not what I meant by interstate competition. Not my area of expertise, I grant.
Insurance companies can compete in any state where they want to do business and where they get licensed or approved or registered or whatever the correct term is with the state's insurance commission. If they think they can make money there then there's no reason why they can't do business.