Price/performance, the quintessential engineering trade-off.
You could trade off battery life for PoE with a boost converter if you wanted, but if runtime or low cost is your key consideration during an outage, then it would be a waste…
I’m interested to hear how the project works for you.
I could have mentioned that there are also active switching circuits that are more complex than an ideal diode that you could use. But again, from an engineering point of view additional complexity didn’t sound valuable.
And I’m a software developer, not an EE.