Small-value and/or micro transactions are arguably never going to work at least in the way most people think about them, though lightning network may succeed in this area, but it's not the most important aspect. Instead, the existence of a money whose supply cannot be increased at the whim of political expediency is the true value.
Maybe you already know this, but there is a strong debate amongst the Bitcoin "community" of whether to accept higher fees, less transaction throughput, but greater decentralization and security or to worry a lot about fees which are rising, and increase the block size "now" because a lot of these people are upset about fees being too high for small value transactions such as the ones you seem skeptical about.
They would argue the tradeoffs aren't that bad, and also that scaling on chain can be achieved to allow for high throughput and low fees. Many don't think this is possible to even approach the volume of something like Visa so why bother and besides 10 minute block times make retail purchases challenging anyways.
Immutability comes with the territory of irreversible and unforgeable. Why you need immutability gets into the argument of why proof of work is the only way this system can work. The double spend problem, consensus, the decentralized blockchain etc etc which I'm sure you're familiar with but anyways
I encourage you to read the Gilder book, it's not that long and he's well known for seeing innovation trends before many... the value of sound money is pretty profound in my opinion. The fact that not only is Bitcoin scarce but completely explicit in its monetary policy (though there will be lost coins that fudge this a little) provides the best form of money as measuring stick that we've ever had.
TL/DR* You don't for small purchases, that use case is already solved today. Finite money supply serving as superior store of value is the point.
and why do we care about those?
Finite money supply, I get. I'm not I agree but I get it.
Why exactly do I need an immutable record that I paid some guy 10 bucks for a souvenir shirt at a concert? That I stopped and grabbed a coke at mcdonalds on the way home. That I went and bought some legal weed.