Sidechain? I'm confused with that Paul Sztorc blog.
But "second layers of batching, you mean = State Channels and Rollups? Because if that's it, OK. Everyone understands that.
What/how does it mean for you to "scale" the network?
Scaling is directly related with compression. If you can use the same resources to achieve more goals, then that thing is "scalable". So, if the size of the block is 1 MB, and your "scaling" is just "let's increase it into 4 MB", then it is not a scaling anymore. It is just a pure, linear growth. You increase numbers four times, so you can now handle 4x more traffic. But it is not scaling. Not at all.
Scaling is about resources. If you can handle 16x more traffic with only 4x bigger blocks, then this is somewhat scalable. But we can go even further: if you can handle 100x more traffic, or even 1000x more traffic with only 4x bigger blocks, then this has even better scalability.
Also, scaling is directly related to intelligence. You can read more about Hutter Prize, which was advertized by Garlo Nicon some time ago:
http://prize.hutter1.net/
Plus what made resource requirements increase if enough users are paying < 1 sat/vB fees?
If you lower minimal on-chain fees,
then there will be more on-chain transactions. Which means more traffic in mempools, less portion of broadcasted transactions confirmed on-chain,
But if there's going to be more on-chain transactions, and more traffic in mempools, wouldn't that also mean the fees go up as well, which could then make demand for block space lower?
It will be the usual situation as if the fees are 1 sat/vB or higher.
My question was thinking more about the Dollar cost of a transaction if the price of Bitcoin surges to seven digits.
and also more pressure, to increase the maximum size of the block (which if would happen, then it would mean, that people decided to scale on-chain, instead of scaling off-chain; and then, it would change the direction in which Bitcoin is going since 2017, by deciding to not scale on-chain).
I believe not. We saw dick pics and fart sounds flood the mempool, and fees spiking to 150 sat/vB. There was no "pressure" to increase the block size. That debate is over, the big blockers lost.