This is a good question and perception plays a strong part of it as well as the country and government.
In some cases, this is how we perceive it. Other cases, population density can be a drawback for some issues, like healthcare or school. Using your medical example, in a system where the government provides healthcare, a smaller city may seem to have more access to healthcare because of its population size to doctors, like a town of 1000 and 2 doctors (500 to 1) compared to a town of 100,000 and 120 doctors (833 to 1). Also, in these cases more people could spread a virus or disease faster, meaning that a higher density of population has more need. We can see this in some cases in smaller cities with transportation - it appears they have better transportation in some cases, but how many people are driving that often? Not much at any given time.
School can be very similar. Some small schools in rural areas can be really good with some skills at teaching because they have fewer students, so teachers can give more attention per student. Exceptions here exist as well, but if we're talking about government funded education this can be a pattern we see.
There are many exceptions to this. For instance, areas where people love to live (water), we may see higher ratios of doctors or educators, so these cities may tend to do better than other cities as far as access. Geography and weather will really depend - keep in mind, doctors have many options, and they can live where they want. As for capital cities, it depends. More internal or cold capital cities always seem like they need more help than capital cities on coasts and in warmer climates (or so it seems).
A good way of assessing this is just ask yourself where do most people ideally want to live? Then ask, with some skills (medicine) that have the flexibility to live where they want, where will they probably be? That will help you identify where bottlenecks in highly-skilled labor tend to appear.