Well, for starters this is decidedly and completely untrue.
But moreover, when your phone dies and you're using it as a remote at home, you likely have the charger right there are home too. When the AAAs in your dedicated remote die (though PERHAPS more infrequently) you need to go running around to see where you shoved that container of AAAs, find that they're all actually the dead ones, and then go to the store.
Perhaps? Why are we beating around the bush, does your remote battery die enough that you even have a concept of how long the battery lasts (I don't. Is it 6 months, a year, 2? No idea, too infrequent to expend brain-space on)?
Battery is only the second worst part about using a phone as a remote, the worst being that a phone is anti-social while watching television (on a television) is social.
My phone is the one device I know will always have battery, because it is important enough for me that I always charge it. It's also the one device I know I will always have near me.
What kind of geek doesn't have a USB charging port or two built in to (or close enough to) their couch? Couch charging has been the default for my wife for ages...
Bad argument. Any remote control can run out of battery.