The problem is a bit more complex than simply overloaded servers, especially since one of the newer 'servers' is actually several very high performance download sites spread around the world.
The stock explanation of 'overloaded servers' has really never been complete and is less likely to be the real cause at this point. A better description might be 'server unavilable', since this covers all the bases involved.
The reason is that only a couple of the current servers are often truly overloaded, the real problem is usually something else like network (Internet) issues or even occasionally problems at the users own PC. There have also been other transient issues like upload failures of some files to some servers, though these occur less often.
Though the addition of the worldwide servers has helped, there are still lots of network peering issues, especially in less developed regions like Asia and in fact much of the entire continent all the way to Europe. Only the several servers in the European region keep it from having similar problems. What this means is your ISP isn't 'well connected' to the networks where the servers are, which may be temporary due to failed networks between.
Despite the multiple potential issues I've mentioned the 'solution' is the same, try a different server, since that's the only option you've got anyway.
As for the idea of automatically switching servers to one that's 'available', I know this has been proposed in the past, because I did so myself. My suggestion was to attempt to download a small control file from a server first, followed by the other files if successful. If a file fails, move to the next server in the list and try it again, continuing on through the list of files to download. Of course, you could still select a 'Preferred server', which would become the first server attempted in the future.
This solution would be relatively simple to implement, help to 'load balance' to some extent and should reduce the number of complete failures to only those who are currently cut off from all servers, usually due to transient ISP networking issues. There would still be 'timeouts', but only one per failed server rather than all files attempted and it should be easy to abort between files if desired.