Given that they end up with a breath test anyway, either there on at the station, and the field sobriety isn't typically admissible, I suspect that they do it for other reasons. It's either theatre to intimidate the suspect, or an excuse for overtime for the other 2-4 offices that show up
> Given that they end up with a breath test anyway
You might not have a lot of say in whether you’re taken in for a breath test, but that doesn’t make it admissible in court. A cop only needs reasonable suspicion to pull you over and ask if you’re drunk. A cop needs probable cause to arrest you for breath test.
The purpose of the field sobriety test is to help with the probable cause part. It’s also worth noting that (in the US at least), you are never under any obligation to participate in one. Refusing one can’t be weighed against you as probable cause, and participating in one will never help you. Especially considering police will judge as sober field sobriety test participant as impaired about 50% of the time.
Roadside breath tests are quite a different matter though. But they’re still used for the same purpose. The actual evidential test will be a blood/breath test performed after arrest.