That's not entirely accurate. His solution was to increase the block limit [1], and use faster computers [2]. Note that Bitcoin Cash is currently implementing this, and succeeding at scaling to 1,100 tx/sec on testnet. (Bitcoin Core supports 3 to 7 tx/sec.)
[1] "It can be phased in, like:
if (blocknumber > 115000)
maxblocksize = largerlimit
It can start being in versions way ahead, so by the time it reaches that block number and goes into effect, the older versions that don't have it are already obsolete. When we're near the cutoff block number, I can put an alert to old versions to make sure they know they have to upgrade."
~ Satoshi Nakamoto, on bitcointalk.org, October 04, 2010, 07:48:40 PM
[2] "Hi Mike,
I'm glad to answer any questions you have. If I get time, I ought to write a FAQ to supplement the paper.
There is only one global chain.
The existing Visa credit card network processes about 15 million Internet purchases per day worldwide. Bitcoin can already scale much larger than that with existing hardware for a fraction of the cost. It never really hits a scale ceiling. If you're interested, I can go over the ways it would cope with extreme size. By Moore's Law, we can expect hardware speed to be 10 times faster in 5 years and 100 times faster in 10. Even if Bitcoin grows at crazy adoption rates, I think computer speeds will stay ahead of the number of transactions.
I don't anticipate that fees will be needed anytime soon, but if it becomes too burdensome to run a node, it is possible to run a node that only processes transactions that include a transaction fee. The owner of the node would decide the minimum fee they'll accept. Right now, such a node would get nothing, because nobody includes a fee, but if enough nodes did that, then users would get faster acceptance if they include a fee, or slower if they don't. The fee the market would settle on should be minimal. If a node requires a higher fee, that node would be passing up all transactions with lower fees. It could do more volume and probably make more money by processing as many paying transactions as it can. The transition is not controlled by some human in charge of the system though, just individuals reacting on their own to market forces.
Eventually, most nodes may be run by specialists with multiple GPU cards. For now, it's nice that anyone with a PC can play without worrying about what video card they have, and hopefully it'll stay that way for a while. More computers are shipping with fairly decent GPUs these days, so maybe later we'll transition to that."
~ Satoshi Nakamoto in correspondence with Mike Hearn