I'm British, have lived in Ireland for many years. While I miss many things about the NHS, I don't miss the long waiting times for an appointment with my GP.
Here I pay €60 for a GP appointment, more if they take bloods, or €30 for a repeat appointment about the same issue. We get tax relief at 20% on the cost, or can claim a proportion of it back via private health insurance. I certainly think very carefully about whether or not I really need an appointment. On the plus side, in an emergency I would be seen the same day or the next day. If I need a routine appointment and want to see a particular GP it can be a week or so.
I don't know the percentage of missed NHS appointments, but for Ireland, a quick Google picked up this:
'Missed GP appointments, commonly referred to as "Did Not Attend" (DNA) rates, typically range between 4% and 6% in Ireland. This translates to a loss of 1 to 2 appointments per day for an average GP, with higher no-show rates heavily correlated to patients holding medical cards.'
Medical cards, which give free GP appointments and various other benefits, are means tested, and are also available to children under 8, pregnant women and everyone over the age of 70 as far as I'm aware.
I also read that 42% of people in Ireland have medical cards, so that's a substantial proportion of the population who are entitled to free GP care.