A couple things, Hades isn't a good comparison since it has a pretty good optimized android port. You won't get nearly as favorable a comparison on other games if one's running on the Deck and the other is running through GameNative. The FEX compatibility layer will have a performance hit vs running on x86 hardware, although I don't know if anyone has found a good way to measure it yet.

For RAM, the S23 has a slower memory bus than the deck, and Android + background processes will typically use 4-6GB of the system RAM. So you're generally left 6-8GB for your combined RAM/VRAM, accessed at a slower speed, which will severely hamper a lot of more modern games.

For TFLOPS, phones are usually rated at a peak rating, rather than something that can be consistently sustained. A big part of this is thermals, which an external cooler will help with a lot. But you're still going to probably have pretty significant decrease in performance outside of those peaks, typically only 50-60% of the peak power. There's also practical TDP limits, even high end phones have a max TDP of 5-7w vs the Deck's 15w limit, which will limit how much it can run.

It's also just kinda nice to have a separate, low fuss gaming device. I can grab up the deck and immediately continue playing where I left off in seconds. I used to play more games on my phone before the deck, but I had constant issues with calls and other interruptions making it hard to get proper play sessions in. I typically gave up on playing any game that didn't have save on exit, because of all the lost progress. And your setup sounds like it takes longer to setup, needing a cooler and controller setup each time you go to play.