Thanks for the suggestion! We did consider the idea of making it automatically cut the energy source. However at the moment, the install steps are: receive it in the post, pull out the battery tab, and stick it on your stove splashback with a strong sticky pad. Almost anybody can do it themselves. As soon as you need to cut the electricity/gas it requires a qualified engineer to go in and install it, making the install cost an order of magnitude larger. So this wouldn't be a part of the core product.
As an optional paired peripheral, it's a good idea, and perhaps we will look into it further if the main product has some success. If individuals consider it a valuable addition then they could pay to have it installed. A secondary drawback would be reduced battery life on the device, as it would be continuously paired over Bluetooth whenever the stove is in use - usually it is just passively advertising in case you are trying to connect through the phone app.
In terms of saving lives, the automatic cut-off would make a relatively small difference - fire department stats (on smoke alarms) show that having a loud beeping alarm is extremely effective at attracting attention and is enough for the user to go and turn it off manually, or to get out of harm's way if things have turned bad. Where the automatic cut-off would help is in reducing the chance of the house being damaged by smoke or fire when the user is out of range.