Drink driving/Speeding?

Why is a person entitled to a duty solicitor (free of charge) to represent them in court if they get caught drink driving, yet if they get caught speeding and have to go to court, they are not entitled? They are as dangerous as each other.

It's the potential penalty that determines your right to counsel. If a person's liberty interest is threatened, they would likely be eligible for a duty solicitor. If it's just a fine or monetary interest, they're on their own.

Because you can go to jail for drunk driving, you can't for simple speeding.

In the US you can get a lawyer for any charge, but usually speeding is a misdemeanor and you cannot be jailed for it.

Because it's more serious they usually need legal advice, they can end up in prison for that.

You can receive pro bono legal council for both in the US. Because a DUI involves an arrest, trial and possible jail time, it is assumed you will need representation. A speeding ticket is normally resolved without a trial, but if your were to request one, legal council would be provided upon request.