The cats are too fast under indoor lighting, even when they just sit there only moving their heads. Our dogs were the same way. Even with my cell phone, I often get a little blurring because they won't sit completely still. I use the flash because the colors are better that way, though it throws off the contrast & saturation, and the pre-flash leads to closed eyes. They're not good pics either way, lol. I do have a few rolls from my GS-1 I've not developed yet, and I'm confident those pictures will be quite good.
I do have a good flash bar for the SX-70 that I found at a thrift store, but I'm saving that.
I've seen people take really good pictures with an SX-70 regardless of situation, but those people have skills (as shown in the OPs video).
Otherwise, I find the older Polaroids are best used as intended - quick little snapshots. They are fun cameras, and you can't beat the reactions and smiles you get when you hand someone an instant photo.