Airplane mode cuts off all or non-wifi communication, which is undesirable. Receive-only mode would allow receipt of texts and recorded messages, save power and prevent detection of the phone by radio frequency methods (not by a metal detector). If the phone is stationary, then there is no need for it to send periodic keep-alive or hand-off signals to the cell phone tower. The phone’s accelerometer and GPS receiver can detect with reasonable accuracy whether it stays in the same cell tower’s range. Only when the phone moves a large enough distance will sending hand-off or check-in signals become necessary.
Location can also be detected using the radio receiver of the phone (which every phone has for calls and texts) if multiple cellphone towers are in range – just triangulate. A saved map of tower coverage areas in the phone helps position the phone and detect when the phone moves to a different tower’s area.
A software modification should be enough to create a receive-only mode: turn off sending (supplying power to the antenna) but keep receiving (measure and record the voltage and current in the antenna). Add optional deactivation of the receive-only mode based on the accelerometer and GPS detecting the phone moving out of range of the current cell tower.
Given the two objectives are: (1) save power and (2) prevent detection of the phone via RF methods, I’d argue that (1) effect would be extremely weak, if not negative for most metrics, and (2) is irrelavant for the vast majority of consumers. For the latter, I am not sure when this criterion could come in relevant. I am, or at least was, a privacy geek, and this concern has never crossed my mind, except for singular border-crossing occasions, when it was easier to turn the phone off completely.
For the former: from the network viewpoint, this sounds like making the “stay-alive” connection timer very large, so the network tower keeps sending packages to the device assuming it is alive, without the device’s response. This turns a waste (of the tower’s energy use) when the device in question has been turned off or loses network, which I’d say is not a rare occurrence. Saving the device battery at the cost of the network tower battery consumption sounds dubious in this case. On the one hand, from the pure energy use standpoint, my guess is that this tradeoff is extremely unfavorable. On the other hand, from the consumer convenience standpoint, this probably does not add a whole lot, since when a phone is stationary, on most occasions this implies the consumer has charging opportunities nearby.
On the device side, keeping active track of accelerometer data is probably already something most devices do for other use-cases, so this would not increase energy consumption by a lot. However, my impression is that active GPS tracking is extremely power-consuming, much more so than maintaining a keep-alive exchange with a network tower.