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While I recognize the tenet of your argument it is not complete in itself and so is flawed. An unqualified "high population density is not a problem" is as inaccurate as a unqualified "high population density is a problem".
If you dig deeper into the population theory, the demand/supply equation still needs to be sane. So while population density in itself is not a problem, any resource scarcity because of population is a problem.
Taking that argument further, it means that the GDP should meet the requirements of the population and unemployment must be low to ensure that the GDP is really creating the means for consumption for each individual. This needs the population density being primarily made up of younger or productive population. If conditions like those faced by Japan, parts of EU and US in terms of declining productive population is replicated in highly dense countries, the country will not be able to sustain that population.
So as you point out people move to cities but if you ponder why it is for employment or enterprise opportunities. If the city is converted into a soveriegn state it will be great and the population will be sustained in a great way. For instance if you create a country out of Maharashtra and Gujarat you will not have to worry about population as the productivity can sustain it. But when these cities have to produce for those areas which do not have productivity and sustain that population as well, there is a problem.
So if your population is growing more than the growth of productive workers then the economy will get hit and the slogan on the website is appropriate. But as education and thus productivity increases population may be a boon.
So a population density in a productive state with growth more than the population growth is fine actually good but not so good otherwise.
Email me at sachin.vora@gmail if you want to discuss in depth.
Sachin