They do. But they often insist on sobriety tests anyways, because it helps them gather circumstantial/subjective evidence against you. Basically, a breathalyzer will objectively say if you’re over the limit, but a sobriety test allows the cop to feel like you’re over the limit and arrest you even if you’re not.

The breathalyzer removes any subjective doubt, so cops will often use it to confirm when they obviously know someone is over the limit. But they don’t start with it, because keeping that subjective doubt as long as possible means they can keep probing for other reasons to support an arrest in the meantime.

Basically, imagine you’re an investigator doing an interview. Your job is to arrest this person, even if they have done nothing wrong. If you open the interview with a breathalyzer, you remove any doubt about their sobriety when they blow a 0.00. But if you start with a sobriety test and they “fail” (by your subjective, totally 100% biased opinion) then you can initiate the arrest before you even breathalyze them.

And even if they blow a 0.00, you can say that they’re high instead, (because they “failed” your sobriety test), and arrest them to take a drug test back at the police station. Since the drug test isn’t testing for active impairment, (it’s just testing whether or not they’ve done drugs in the past few days/weeks) there is a much higher chance that they’ll turn up positive on the drug test even if they’re sober. But again, you don’t actually care if they’re sober; You just care that you got the arrest, and that they pissed hot on a drug test back at the station because they smoked weed last week.

Americans do have the right to refuse a sobriety test, and they should! Cops will push and make it sound mandatory, but it’s not. Just insist on being breathalyzed instead. Because a field sobriety test (even if you’re stone cold sober) will only help the police form a case against you. And under your fifth amendment rights, you’re not required to help the police build a case against you. Field sobriety tests are the “I’m saying I caught a whiff of weed coming from the vehicle, so I can justify ripping your entire car apart on the side of the road even if I don’t find anything during the search” of DUI stops. Cops will use it to justify an arrest even if you have done nothing wrong.