Radio transmit is expensive power-wise. The numbers I'm seeing for BLE energy per bit are all over the place, but the numbers I found for some SHA3 testing say that even with a pretty old chip fab you can make a circuit that encrypts more than 10 bytes per nanojoule. That's a pretty small tax.
Not to mention real-time broadcasting of sensor data to multiple devices.
In the case of HR data: ~1 update per second which is usually broadcasted three times in succession to ensure transmission)
30 seconds of searching shows me the polar h10 is already multiprotocol and supports Bluetooth.
https://www.facebook.com/dcrainmaker/posts/pfbid02doLyLhNSwT...
The next time you buy health insurance or are involved in a court case the data may be used against your interests. (probably someone can invent a still more nefarious scenario)