Respecting known limitations and working within best practices is absolutely not premature optimization. If you know that using the mobile radio in a certain way is a source of excessive battery usage, it's silly to just disregard this information. It's not premature optimization if you know where the performance issues are from the outset, and these performance issues are so incredibly common that the Android team put out videos about them.
The mobile radio will eat your battery very quickly, and probably chews through as much power as your screen. If you want to see how expensive it actually is, disable fast dormancy†. A slightly less brutal demonstration can be had by opening an OpenVPN connection. The keep-alive packets will keep your mobile radio in a higher power state, pretty much in the same way some disrespectful apps do and you'll (quite unsurprisingly) see your battery drain faster.
A badly written app can drain hours of battery charge, not minutes.
> Your users will be better served by you fixing bugs or adding features.
Excessive power drain is undoubtedly a bug. I absolutely love apps that respect the fact I want to go as long as possible without charging my phone. I might often be in a position where I can't charge my phone too. (Carrying a second or third battery is useful, if you've got a phone that has a replaceable battery.)
> Really, unless you're a huge team with a huge budget...
It's quite trivial to think about performance and battery life. This is something every mobile developer should be thinking about from the get-go anyway, and if you can't afford to write an app that performs well, you can't afford to write an app.
> Making battery usage the prime concern for most apps is overkill.
I'll uninstall apps that I identify as too power hungry without a second thought, and I'll also write negative reviews too. I'm pretty sure that when put in this light, power consumption suddenly becomes important.
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† Don't do this. Some phone networks are misconfigured and may fail to ever recognize that the phone is FD-capable again.