If you happen to be an entrepreneur, a foreigner (relative to the country of work), or an American citizen (despite holding the citizenship you're on, thanks FATCA!), then, yeah, I can see why you have never encountered the simpler arrangements.
If you're an ordinary citizen of most countries and work under a company, the company is obliged to track it for you. What you get is a very simplified form asking if you have more income sources than from your work, and the local tax system means that most of them legally do not have any (for example, banks collect the taxes for the interest you have received, not the arcane American system where you're the one responsible for that).
In a PAYE system, merely being a foreigner isn't _usually_ an issue, provided that you're domiciled and don't have foreign income. The exception, as you mention, would be a US citizen; the US's approach to foreign income of its citizens is sufficiently weird that they'll generally have annoying tax situations.
> What you get is a very simplified form asking if you have more income sources than from your work, and the local tax system means that most of them legally do not have any
If even that. In Ireland, and I believe the UK, you only have to fill out that form if you actually _do_ have non-employment income which is not deducted at source. Most peoples' only interaction with Irish Revenue would be to claim tax credits on rent/mortgage/medical expenditure/whatever.
If you're an ordinary citizen of most countries and work under a company, the company is obliged to track it for you. What you get is a very simplified form asking if you have more income sources than from your work, and the local tax system means that most of them legally do not have any (for example, banks collect the taxes for the interest you have received, not the arcane American system where you're the one responsible for that).