Having been both a doctor and patient in both private and public hospitals in Ireland, I would not get rid of my health insurance.
I'm not surprised that a consultant may say they don't have VHI, are happy to use only the public system, etc., because when you have direct access to the system and all of your friends and colleagues are doctors and nurses you are guaranteed a very good service!
Staff in Irish hospitals are very well trained by international standards. I have worked abroad in Europe and USA and Irish-trained doctors and nurses are highly regarded. Consultants in Ireland tend to train longer than anywhere in the world and are much more likely to have done a PhD or other research degree. We have a very high density of consultants who have trained abroad at big international centres in London, New York, etc. so your local consultant in Ballygobackwards General Hospital is quite likely to have done a fellowship in one of the best hospitals in the world. Most people are not aware that we have such a calibre of consultants here - or at least we did until the latest contracts came in, but that's another issue entirely.
In public hospitals, health insurance gives you preferential access to better accommodation but much more importantly it gives you better access to procedures. If a consultant has a theatre list and can perform 10 procedures on that list, their contract may allow them to do 2+ private cases on that list of 10. Straight away the public patients who have private insurance have a 25% better chance of getting a spot than someone without insurance. What is worse, if the consultant decided to do 10 public cases, they would be taken to task by management. Why? Because the hospital can charge the insurance company a large sum for each private case done - so public hospitals have a perverse incentive to treat private patients.
I regularly hear "It's a great system once you're in, the staff are great, etc." but that is not what a health system should be like. Public and private systems should be totally separate and everyone should be either be covered by an insurance system like in the Netherlands or from the public purse like in the UK. That way everyone has equal access at the point of care and your job or your daddy's bank balance or any other privilege won't affect your care. Having worked in the NHS and having been a patient in that system, it is overall much fairer and better value for money than the Irish one.
Edit: We still have a funny attitude that public patients should be somehow grateful for whatever they can get "Oh you were lucky to only wait 6 months" etc. That is not how it works in private hospitals. There is a fine balance between being engaged and being unreasonable, but public patients really do need to start demanding hospital CEOs and TDs to give them the resources that they deserve. Doctor and nurses unions and training bodies actually spend a lot of time advocating for patients, but what we really need is a well organised public protest like the water charges. I think the public don't truly realise how badly they are being treated (pardon the pun).
