In the US, the cops try very hard to question you (for hours) without one. And while there is a public defender system, it doesn't usually provide a competent lawyer.
This is well documented in the (very readable) book "The Secret Barrister". https://thesecretbarrister.com/
The author claims that the cuts are not even cost-effective, often leading to more spending by government to deal with the consequences.
But what actually happens is that the system makes them incompetent simply being in the job. For example, the caseload is too high, which means that they cannot spend the time a paid lawyer would spend on it. Folks also get little choice in which of these cases they take and which they do not. On top of all of this, they are working in a system stacked against them and they usually aren't getting paid much.
Public defenders also get far less resources than prosecutors.