Is it actually Instagram Reels that is inauthentic, or is it the content that people post there? The Instagram Reels service is just that - a service people can use to post videos, same as TikTok. It's the people who choose to use the service that cause it to seem inauthentic, not the service itself. If everyone migrated from TikTok to Reels overnight, then wouldn't Reels become more "authentic"?
"The algorithm" doesn't matter as much as you think it does. If all the videos have metadata, it's quite simple to suggest another video to someone if they just watched a similar video. I watch how my wife uses TikTok, and "the algorithm" is hit or miss. Most of the time it's a hit, but that's because the metadata from the preceding videos (and how long she watched them, or didn't) makes it easy to figure out what she'll most likely want to watch next. Without metadata, there is no "algorithm", and with metadata, it's trivially easy for anyone to produce "an algorithm" that does the same thing, maybe even better than TikTok does it now. I mean, if you do a search about how to put on makeup, then the next 10 videos you see are going to be about how to put on makeup - that isn't exactly an irreplaceable algorithm.
The content doesn't matter. There's more than a lifetime supply of I'll relevant kinds of content on both platforms. The algorithm for curating your feed matters.