I'm not sure if satoshi makes bitcoin as an alternative payment system, or with the intention to create the best and most used payment system, but this second option is impossible by the bitcoin nature and i will explain why.
If bitcoin want to become the #1 transactions and payment system it would have to be really more powerfull. If we compare the daily transactions banks vs daily transactions bitcoins, then you will understand why i call satoshi visionless:
I'm not sure Bitcoin was ever intended to compete with Visa. It wasn't just designed as a payment system, but rather
money, which is a far more impressive feat. I think
this post by Satoshi really gets to the heart of his vision.
Also, in theory, Bitcoin could compete with Visa. Lightning or some other off-chain mechanism that allows for exponential scale will be required, though. I recall reading that Satoshi actually included payment channels in the original Bitcoin client, but they were removed because they were insecure.
Having a low TPS volume means more scarcity,which leads to bitcoin having more value as a "store of value" type of financial asset.
It's scarcity of the currency supply (the 21 million coin limit) that does that, not scarcity of transaction volume.