The batteries in the original SX70 film packs were amazing. Though they were never advertised as being rechargeable, they can be recharged. I don't know about the current ones in that regard.
Indeed they were, the original Polapulse batteries were another technological achievement we can attribute to Polaroid. They weren't only used in Polaroid cameras either, Sinclair in the UK made a small portable television set that used the Polaroid batteries to save space, Polaroid themselves made a portable AM/FM radio that could run on used film packs:
https://www.radiomuseum.org/r/unknown_polaroid_600_plus.html
Despite their small size and zinc-chloride chemistry (the same chemistry as modern "heavy-duty" batteries) the Polapulse batteries had impressive discharge characteristics. The battery only had a capacity of 264 mAh, but had a very impressive 15 Amp instantaneous pulse current capability. This is of course necessitated by the design of the SX-70. When a picture is taken using the camera, a lot of current is needed immediately to activate the autoexposure circuits, close the shutter, flip the mirror, stop down the lens, open the shutter again, close the shutter again, drop the mirror, open the lens back up, open the shutter again, and activate the gear train which ejects the film and pushes it through the roller. Also to provide power to a flashbar if one is inserted. It has to do this only ten times, but every time, and in adverse conditions, and is thus overbuilt.
The technical details of the original Polapulse battery are available here:
http://forums.parallax.com/discussion/download/36529/P100.pdf
Now if you open up a used pack of film from Impossible/Polaroid Original, you will find a battery marked "Impossible Impulse Battery model I-11", shown here for reference:
https://www.aliexpress.com/i/32956840091.html
Opening the Impossible battery you find two 3V lithium cells wired in series for the neccesary 6V that the camera runs on, the model number for those cells is CP225040N. I have attached the links for two datasheets below. What you learn from these datasheets is twofold. First, the battery does have a higher capacity than the original at 750 mAh, versus the 264 mAh of the original. However, the pertinent characteristic is instantaneous or pulse discharge current, and that is where the replacement battery falters. Where the original battery could provide 15 Amps instantaneously, the new cells have a stated maximum pulse discharge current of 500 mA or 0.5 Amps. It is severely lacking in this regard, and I have encountered numerous occasions in which the battery in a Polaroid Originals pack has failed to cycle the camera fully in a partially used pack.
http://www.gmbattery.com/Datasheet/CP/CP225040.pdf
(Photrio has removed second link)
The battery used in these new Impossible batteries is a Li-Ion battery so they are indeed rechargeable, however care must be used as LI-Ion batteries require specific charging regimens to prevent incident. They are also notoriously more flammable than the original Zinc-Chloride battery although, thankfully, I have never heard of incident as a result of this.
One other item of note is that the new Impossible batteries are noticeably larger than their Polapulse equivalents, I have no doubt that this is the real reason why Impossible/Polaroid Originals packs only have 8 images in them instead of the original 10. I never really bought into the reason that Impossible/Polaroid Originals gave which is that the film is thicker. The reason being that if the film were thicker, then the rollers would need to be redesigned to allow the film to pass through with the appropriate amount of pressure. If you read about the problems that Polaroid had with roller clearances when they brought out type 38 Polacolor roll film, then it becomes apparent that a thicker film stock would not function in unmodified cameras. Measuring with a digital caliper also confirms that the film is the same thickness as that sold by Polaroid before they ceased production.
