My cellphone needs more than 1 day to drain and I'm playing Hearthstone with it while having 4G, bluetooth and wifi on at all times. You need to get a better phone. Wireless transmission is extremely efficient nowadays and will only consume a tiny fraction of what the display does, which is what the battery pack is mostly for.
The battery pack is just huge because the Vive is not meant to be used wireless and has as such zero energy saving features and hardware, let alone proper compression. Also because it's external and not integrated. A proper headset that's designed for wireless use is gonna be just fine.
Isn't hearthstone a 2D game? I know Switch drained rather fast while playing Zelda and that only has one 720p screen. A good next gen headset should start with dual 1440p screens. For wireless it can't use a lot of compression as any compression artifacts will be very noticeable when blown up to 150 degree stereoscopic view and interfere with the stereoscopic effect as well. dual 1440p at 90fps is 1.85 GB/s uncompressed. Some compression is required plus using multiple 5GHZ channels to get all that data across. Then enough processing power in the device to handle decompressing and displaying that 1.85 GB/S dual 1440p image at 90hz.
It's not comparable to your phone playing a 2D game on a single screen while occasionally sending a wireless data packet.