Yea I don't think telling people to move to a different data centre is providing a good solution. Yea sure they can get a house but they also have to leave all their friends behind. There is no cross data centre visit, no cross data centre party invite system, and you can't even hope to bump into your friends from another data centre in DF. Even worse for players who would be going to a data centre for a different region because that can mean noticeable lag, depending on their location and the internet that is available to them. Certainly that would often be the case when dealing with distances as large as North America and Europe.
As an aside I think partially why EU has less population issues is because the population is more evenly distributed due to languages. In NA the majority of people there are North American, which means English is their native language most of the time. In Europe this is not the case due to the large amount of languages spoken there. For example it is well known among EU players that French speaking people tend to play on Moogle and Louisoix. SE said when they were selecting servers to put into Chaos and Light they thought about the language groups the communities made on the EU servers. So what ended up happening is the servers with large French speaking communities ended up in Chaos, and those with large German speaking communities ended up in Light. Basically what I'm saying is due to the nature of how Europe is as a region linguistically speaking, servers naturally get more even population distribution. There are of course some population issues on some servers, some related to housing, but none anywhere near as bad as the likes of Balmung.
Also as far as I'm aware NA has less breathing room than EU and JP when it comes to the amount of servers available for the size of the overall region's player population. So even if there was a more even distribution of population, there would still be a very noticeable shortage of houses.