Unless you're going to put chip readers in every place of public accommodation, this won't help much.

it wouldn't be hard or expensive for places that care about allowing service animals to get a chip reader.

Every place of public accommodation, i.e. all businesses, are required to allow service animals. "Caring" isn't optional.

many places don't care to exclude pets at all. they don't care. many places might decide its not worth caring about if its a real service animal or not. they don't care. the only places that care are the places that would want to actively exclude non service animals.