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https://bitcoin.org/bitcoin.pdf makes it clear that Bitcoin is definitely a payment system, a distributed one. But it's not only a payment system, and using it like one right now is pretty dumb because of the absurdly high transaction fees, but high fees are entirely a temporary artifact as the system scales. (Edit: removed hostility.)

Bitcoin will never work as a consumer-to-merchant payment system. Even with 1GB blocks (1000 times today), it would max out at ~7,000 TPS, where VISA does 200,000 during peak. We need something off-chain to be able to scale to +100k TPS (unless you consider 100 GB blocks realistic).

I believe you're off by 2 orders of magnitude for Visa's seen-peak and about 1 order off for their network's designed max peak. Unless you've got sources more recent than https://en.bitcoin.it/wiki/Scalability uses; maybe you're confusing the number with the network handling all transactions world-wide which Visa doesn't do?

100 GB blocks is politically unrealistic in the foreseeable future but technologically not really, especially because network and storage continue to get better and cheaper even if CPUs are stalling. Nodes don't need to store the full chain, and 10 years of that size of block would only be about 50 PB. Gigabit networks are only becoming more and more common, a 1 Gb connection will let you get 75 GB over 10 minutes (and using the math from the wiki you only need 0.76 Gbps to handle 200k tps). Also not every node needs to see every transaction, the effective bandwidth can be much lower, just like the effective storage.

And as the wiki points out, PayPal has a much lower TPS than Visa or others but is still widely used as a direct consumer-to-merchant or friend-to-friend payment system. In addition, the better straw argument against Bitcoin as a payment system has always been "who is going to wait 10 minutes on average, sometimes much longer, especially if you want the gold-standard 6 confirms, to buy a stupid pack of gum?"

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