Have you ever seen the statistics? The DPAs are massively underfunded and the Irish DPC in particular is notorious for ignoring complaints, to the point where the EU is considering launching infringement procedures against Ireland for not properly enforcing the GDPR. If you think they will take action on a complaint like this, you will get disappointed.
On the other hand, petitioning the courts to intervene is probably easier than you think. In some member states you don’t even need a lawyer, so all it takes is a bit of time and some court fees. I’m not saying it’s the preferred option, but realistically it is the shortest path to a result.