An interesting solution, it has advantages and disadvantages. An advantage is that a leash is independent of the car, which could be an advantage for a person who frequently uses other modes of transportation, such as airplanes, train, etc. But I don't, at least for now.
The biggest disadvantage is that the leash is one more device which has to be charged periodically; if it's part of the car, well, the car already gets charged periodically.
Don't know what gotchas there I might uncover with how the leash might affect the Bluetooth connection with the car's hands free phone.
In the end, I think a separate Bluetooth leash would cumulatively be a lot of work (as in another device to keep charged) to fix a very infrequent problem. The reason for building the alarm into the car is that it would only require me to select the option once, then I'd not worry about it again...