Assuming they’re able to discriminate on the cost to bias against high theft regions you’ll see a lot more pressure locally to fix the problems.
There's no "false pretense" involved in the idea that theft increases the cost of goods for paying customers. The businesses in question appear to be offering insurance which is entirely opt-in. It's not any different from offering an extended warranty.
But even in principle, businesses don't need to be "allowed" to "raise prices to increase profits". Increasing profits is their explicit right, and to some extent even their responsibility (to shareholders). But it turns out that raising prices is often counterproductive to that goal, because prices influence demand. This is both Economics 101 and common sense.
Keep in mind here that we're talking about goods that are being shipped to houses (and possibly being stolen from front porches). Generally speaking, that's not exactly going to include basic necessities.