Its very common for national anthems as sung at sporting events or otherwise to be abridged to the first verse. Its probably got more to do with keeping things short and sweet to be honest. A short sung verse is enough for people to enjoy without getting bored. In the modern world there are also commercial pressures such as the time it adds to programming, this may have an influence as well.

The same is true of the British national anthem, for which just the first verse is sung these days. I'm not so familiar with the US anthem to be honest but the 5 subsequent verses of the British national anthem talk about things such as crushing the Scots which would be pretty inflammatory if sung today!