Public services not coping with demand isn't necessarily a sign of overcrowding so much as systems in need of reform, whether it be small or major reform.
Personally, I walk through the countryside and don't have a problem bumping into people. I also walk through cities and the capital without bumping into people. I stroll through private and public buildings without any problem and wherever I am, don't queue for very long at all. Based on this, I don't think we have such a problem with overcrowding as some people make out, and most other problems associated with dense populations can be sorted out without preventing people coming into the country.