Boy, trust me, we'd like it to just work as well. Requiring a customer to configure their router is pretty much the last way that we want to introduce you to the game.
Without being the engineer who came up with how this works, I can only give you the 10,000 foot view of why we did it this way.
First, TCP is good at surviving lost packets, but not so good at being timely. Nevertheless, this is all games were able to use, so they used it. And depending on your route to the server, it kind of sucks for latency dependent games.
UDP is much better for real time data transmission, though it has its own set of weaknesses. Nevertheless, it's better for games like us.
Where the problem arises is from the constant attacks going on in the internet, which means router manufacturers lock down the routers as much as possible. If you're superhuge (Xbox Live, WoW, Counterstrike) they'll sometimes open those ports by default. But otherwise, they require you (the user) to open them.
I know that at one time, our UDP ports were a bit irregular. We did some research, and came up with a different range that was the same as some other popular games/applications, the idea being that more routers might already have those ranges open. I wasn't around for that process, so I don't know why we came up with the range we did, but that was the thought process behind it.
So, the reason we ask that you open these ports, is that we can give you a more responsive game. I look forward to the day when routers could be intelligent, and automatically open ranges based upon user input, much like firewalls do, but that's a ways off. Heck, I'm just looking forward to the day when a router doesn't break by simply throwing half the packets away (a situation we've actually run into).