If block size won't increase, there will be no space for new customers who want to make Bitcoin transactions daily and there are billions of people on earth.
This is precisely my point. If we are billions, then we can't all fit by making on-chain transactions on a daily basis. This is true for 4 MB blocks as much as it is for 40, or for 400 MB. It is only a matter of time before these sizes become considered insufficient as well, and we need to go even higher than that.
And this is the good scenario. For if the adoption (or demand for on-chain transactions) does not follow the block's capacity increase, then the network will not be sufficiently self-sustainable.
At the moment, a slight block size increase is necessary
I agree, but you know what they say. The best argument for 4 MB block size is that we already have 4 MB block size. I would rather have something close to 20 MB, so that the network could be less hostile to people who just want to make on-chain payments, but political issues will arise. It'd give Bitcoin some "breathing space" until the softforks, though, I agree it wouldn't harm (apart from politically).
Normal users, who want to use Bitcoin as a p2p payment method, should be able to use Bitcoin as it is without 2nd and 3rd layers.
"Should" is a complex and problematic verb. One person's actions impact another. If you think about it, your transaction occupies the space another person could use. It might sound exaggerated, but your freedom to make on-chain transactions directly influences another person's freedom to do the same. Just because something is considered a "human right" or "privilege" doesn't mean it comes without a cost. Dictate who should bear that cost, and you've essentially created a government.
Second layer solutions aim to minimize your influence on others' freedom as much as possible. That is the goal, in my view.