Would switching from 3 to 1 second block times also scale the network by 3X?

Well, if block size remained the same, you could store more data, but the easy option if we want to scale to process more data would just be to increase the block size.

This latter option doesn't even require a code change: if enough witnesses vote to increase the block size, it will increase automatically. The "con" to increasing the block size is just that it means the blockchain can grow faster and right now the block size puts an upper limit on that growth, so it can be viewed as a "safety net" versus a spam attack.

But increasing the block time offers another benefit that can't be gained by increasing the block size: decreased latency between when a transaction is broadcast and when it is accepted into the blockchain.

This can be interesting for things like games. A game will wait until a transaction gets accepted into a block before it will fully process it. So with the block time being 3s, the game will process the transaction about 1.5s (on average = 3/2s) after the transaction is broadcast, with a worst-case time of 3s (that's a slightly simplified model, but let's go with it). With a block time of time of 1s, the game will respond in about 0.5s (on average = 1/2 s), with a worst-case time of 1s.