I would love to know how legally and practically this all works in Canada. I feel like it may be very similar, but different enough to matter.
Any informants they place in your cell with you, regardless of you asking for a lawyer may continue to interrogate you as well. Your prison phone calls can also be recorded and used against you, again regardless if you've asked and not seen a lawyer so if you phone your job and make up an excuse why you won't be there on Monday morning, that excuse can be used against you in court. A well known trick is for the police to place you with an informant who offers you a cellphone, because typically you have to call 3-4 people when arrested (family/gf, job, a lawyer) instead of just the one phone call they have to give you (which they don't have to provide until days after you are arrested). This contraband phone will be recorded hoping you say something incriminating, or just hoping you lie so they can prove later you are a "known liar" since most people don't want to tell their employer they've just been arrested and will lie about it.
If we're comparing the US criminal justice system to other countries, another more fundamental problem we have is that we simply have more crime. Not "people are getting busted for weed" crime, but property crimes and violent crimes. That fact implicates a much broader spectrum of public policy critiques about the US than how we manage the criminal justice system.
My guess is that outside the USA your legal protections are likely similar or a bit weaker, but the cops are less likely to be antagonistic. (And even in the USA, it will depend on locality and all kinds of circumstances).
Various incentives exist for police and prosecutors to aggressively put people behind bars. I think these are stronger in the populist US, than in other rich democracies where beaurocratic respectability is more valued.