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prospectively, we don't want to make the blocks bigger, so as not to centralise the nodes.
I don't know who is "we". I would simply say that everyone is free to fork Bitcoin to whatever block size they think is best, and anyone is free to use the fork they prefer. Nevertheless, the majority of people seem to like the current blocksize, that's true.
the normal user won't even be able to use the on-chain because of the costs.
That's a strong statement. How can be sure of that? Keep in mind that, as lightning and other solutions increase their adoption, more and more pressure is taken off the main chain.
Imagining an hyperbitcoinized economy, I could open a few channels worth 3 or 4 times my monthly salary, and use them for months and years to perform most of my financial transactions.
everything will happen on the lightning network
I would change that to a less absolutist "an important percentage of transactions will settle on the lightning network".
it will be impossible for most people to have their own custody... (since on-chain transactions are required) → people will have to rely on some companies or mints. The result is that one cannot use bitcoin permission-less.
This already falls apart with the previous comments. Nevertheless, you are probably right in that many people will rely on companies of mints. But that isn't necessarily bad.
Let's make an analogy with banks since we are more familiar with them. Banks fuck you up because they can. They can because it's an oligopoly (you have no where to run to). It's an oligopoly because new players can't get in because of regulation and corruption. It's a walled garden.
The walled garden is the root of the problem: it prevents free-market competition from taking place. You see, in a world where opening a bank was as easy as opening a lemonade stall, there would be plenty of competition. As the market matured, there would be plenty of great entities with an outstanding track record. You would have plenty of options with low risks of being rug-pulled or screwed over in various ways.
Take this bank to lightning custodians: it's an open garden, not a closed one. You are going to see more and more and more entities joining the market. You will have plenty of players like Bluewallet/Wallet of Satoshi/Alby/Pouch/etc. from where to choose. You will be able to split your sats across several of them, and if one of them ever does anything stupid, you will have somewhere to run to.
So, you posed:
people will have to rely on some companies or mints.
I argue back: they will have a wonderful market to choose from.