I'm not scaremongering. People here ask for advice, the fullest advice is the best, including any potential pitfalls. The fact that unlimited 3rd party cover may not apply is important & relevant information. What an OP does,armed with that information, is up to themselves; but at least they know.
I see by your info. 'Time' that your are not living in Ireland, and therefore are insuring your car in another country. We would love to be able to do same as the premiums are much cheaper. Unfortunately we have to buy insurance in Ireland from companies that are subsidiaries of 'non irish insurance providers' and are ripping us off because of the Irish Insurance set up.
We buy insurance to be covered in the event of an accident. To be covered ourselves and cover for the individual that you may be involved in an accident with. Cover for our car in the event of damage and cover for the other individual car. This is what we want insurance for..... do other people not want this?
We do not want full cover in Ireland or EU to become 'millionaires' after an accident.... but we do have a nice car and would like it to be covered as well as ourselves in the event of an accident, its not only the person that can be hurt, the car may need a lot of repair work too. This costs a lot, hence insurance.