Re avoiding going to the dentist if you know you have some work that needs to be done such as a broken filling, chipped tooth .... although you can get around it by chewing on the other side, you should get it seen to as soon as possible. Some years ago I had a couple of broken fillings which I left for
ages. When I eventually got to the dentist he told me it was lucky I hadn’t left it any longer as there was decay.
I think teeth are like cars - if you don’t get the repair early it can lead to more problems and more expense down the track.
I know the system is different in the UK. Our dentists are all private. I think those on low incomes might go to dental hospitals for treatment - but I imagine the wait would be years and being accepted might be means tested. I have no knowledge of how it works. A basic checkup with scale and polish at my dentist costs AU$150. My bill was AU$416.

We used to have private health insurance which covered dental but after doing the sums we opted out of that component of the insurance.
My father is a tough old sod. His doctor regularly tries to find something wrong with him, but the best he can manage is to prescribe some medication to regulate his slightly fluctuating BP.