By design, with our wallet, the secret keys are really yours (created from your own entropy) and are always kept offline.
They aren't, though. A phone in airplane mode is not an isolated device, and as I said above, your phone carrier, Google, and who knows who else can still send and receive data to phones which are in airplane mode. Similarly, even if you delete the wallet before turning off airplane mode, there is no guarantee that the files don't still exist and are accessible on your phone's storage, and could be transmitted to a third party at a later date. Cold storage has to be permanently air gapped.
We are still at an alpha stage (that's why we propose to test our wallet with our money). We will obviously release the source code of the app once we are past this stage and publicly release our product.
Fair point.
Instead, our only incentive is to play by the rules and hopefully turn your heir into our customer.
Another fair point. My only concern is your statement that you do not know the value of the wallet - we do not know that to be true until your source code is released.
If we go out of business, we'll use a customary 12-month sunset period
There is no way you can guarantee that. If you go out of business because you don't have any money left, how will you pay for your servers to stay up for 12 months to complete pending transmissions?