Irish here. It costs about €50 - €60 to see a GP unless you have a medical card. €80 is a bit of an exaggeration.
Pensioners, young children and people on low incomes get free healthcare through their medical card.
It works in the sense that you can get a GP appointment when you need it, often within a couple of hours. Waiting days or even weeks for a GP appointment is unheard of here.
The public hospital system has its issues. There is a charge to attend A&E but this is waived if you have a referral from your GP. Care is free after that but there can be long waits for consultant appointments, scans, etc. Urgent care like cancer treatment is generally good. The main issue at the moment is overcrowding in winter.
Most decent employers offer health insurance as a benefit to staff, or you can choose to buy it yourself. Prices start from around €500 per year but a really good level of cover would cost about €1000. This allows you to use the private hospitals.