There's a school of thought which says that since people generally say they want big houses with gardens then that's what we should be building and not small flats in city centre locations. This is intuitively appealing, but the problem is that housing is a composite good: when people buy a home they're not just buying the structure but the location too, and in practice they're willing to trade off one for the other.
The huge price differentials between structurally very similar properties in different parts of the country indicate that people attach a great deal of value to location, and the small flats you see in high-density areas are in large part the result of people willingly sacrificing dwelling space for locational benefits, even if in an ideal world they would much prefer to live in a big house in a garden in the same location.
Making it easier to build more flats in high-density areas makes it easier to find acceptable trade-offs and would be good for people who value central locations, and it would also be good for people who want to live in the suburbs since there will be less displaced demand from the centre. You sometimes see city centre locations trying to restrict the supply of flats and justifying it on the grounds that people say they want to live in houses, but this doesn't get rid of the uneven pattern of locational demand - it just means that high demand in some areas is concentrated on a smaller number of properties so prices go (sorry) through the roof. Trying to give everyone what they say they want (a big house in a low-density area) makes it harder to give people what their behaviour shows they really want (a home that provides some optimum mix of a range of characteristics including structure and location).
There's an analogous situation in transport policy, in that if you asked people what they would like in an ideal world most of them would probably prefer a nice fast drive in their own car from A to B. But the spatially uneven pattern of transport demand means that trying to satisfy this just leads to huge levels of congestion on certain roads. Since what people really want is just a reasonably quick and cheap way to get from A to B, a better policy is to provide public transport on high-demand routes that moves more people without causing (much) congestion.
The lesson is that it's better to understand the aggregate impact of people's choices and learn from the trade-offs that we make, rather than just try to satisfy what we say we would like in an ideal world. Hardly anyone loves buses in their own right, but they do love the ability to get where they want to go. Similarly, most people don't dream of living in a high-density flat but providing these kinds of homes is a vital part of enabling people to live where they want and ensuring that cities stay as affordable as possible.
By the way, none of this is to say that we shouldn't make it easier to build suburban housing too. We should - but the point is that unless supply is increased in response to demand in city centres too then you won't fix the affordability problem.