(IANAL.) This was reviewed by the courts themselves:
> The CJEU confirmed that the Belgian, French and Swedish prosecutors were sufficiently independent from the executive to be able to issue EAWs. […]
> […] Public prosecutors will qualify as an issuing judicial authority where two conditions are met: […]
> 2. Second, public prosecutors must be in a position to act in an independent way, specifically with respect to the executive. The CJEU requires that the independence of public prosecutors be organised by a statutory framework and organisational rules that prevent the risk of prosecutors being subject to individual instructions by the executive (as was the case with the German prosecutor). Moreover, the framework must enable prosecutors to assess the necessity and proportionality of issuing an EAW. In the French prosecutor judgment, the CJEU specifically indicated that:
* https://www.fairtrials.org/articles/legal-analysis/can-belgi...
The question that the OP asks is fair enough, but there's a lot of subtly and 'low-level' details on how things operate compared to the high-level question that is being asked. Also depends on where the OP lives and what he's used to: common law (UK/US/CA/etc) and civil law procedures and laws are (AIUI) quite different.