In the United States a police officer generally needs to have probable cause to believe you have committed a crime in order to arrest you. The primary purpose of the FST is to establish probable cause. Criminal cases have a certain process, and if the State hasn’t done things correct at any point in that process the entire case can unravel. So if the police officer pulled you over without probable cause, then it’s highly likely anything found after that will be inadmissible and the case would be dismissed.
If they pulled you over for a broken tail light but after speaking with you believed you were drunk, they would need probable cause to arrest you. Police are good at covering their asses, so every arrest report on DUI will also typically contain phrases like “suspect smelled of alcohol, was slurring their speech, had glassy eyes” because even without a FST or portable breathalyzer test just the observation that someone appears intoxicated can also establish probable cause. But you want as much PC as possible so if the suspect is willing to do an FST and a breath test you’d certainly want them to, as failing those in addition with the report about how the person appeared intoxicated would get you easily over the probable cause bar.
In the United States though, FST and PBT results are only legally useful for establishing that the officer had probable cause to make an arrest if it wasn’t at a checkpoint they’d also need PC for the stop itself–like the vehicle weaving in and out of traffic, running a red light, having expired tags etc.
Once you get to the police station they have a much larger breathalyzer machine that can be used for evidentiary purposes. These machines are supposed to be rigorously maintained, and calibration records kept etc so there is more of a technical basis for trusting their results although a blood draw is the only way to accurately know BAC, because measuring breath concentration can actually misrepresent blood concentration in some individuals–I personally do not believe breath testing should be admissible at all and the only use of it should be the PBTs that can establish PC. For the actual evidence the police should be required to draw blood for chemical analysis.