Why is the utilitarian justification of police measures clear in principle but very hard to apply in a single case?

Because every case needs a proportionality weighing that is hard to quantify, every decision risks errors in both directions, and it is unclear how strong a suspicion must be before fundamental rights may be restricted.

Three difficulties:

1. Weighing benefit against harm (proportionality): the measure must be appropriate to the danger, but the two sides are hard to put on one scale. How much (potential) public protection justifies restricting one person's (concrete) personal rights?
2. Misjudgements: watching a potentially dangerous person (Gefährder) can wrongly restrict an innocent person, while not watching can let an attack happen. What risk of a wrong decision, in either direction, is society willing to accept?
3. Threshold of suspicion: the usual legitimation is a substantiated suspicion, often confirmed by a court order. How strong must the suspicion be before the state may violate the fundamental rights of a person under surveillance, for example a suspected extremist?

The utilitarian principle tells you what to weigh, but gives no number for when the benefit outweighs the harm. That judgement has to be made case by case, often under time pressure.

Go deeper:

• Wikipedia (DE): Verhältnismässigkeitsprinzip — the Swiss proportionality test: suitable, necessary, reasonable (Art. 5 and 36 of the Federal Constitution, German).