As I understand it, the EU Parliament engages through the trilogues. Once agreement has been reached there, final approval is indeed more of a rubberstamp. (But: I'm just somewhat interested in the subject; I'm not an expert on the process.)
Once an agreement has been reached, the Parliament can still reject the proposed law (which can easily happen because a conciliatory committee does not represent all the factions in parliament and of course public outcry/petitions can change opinions).
You’re conflating two things. Yes, the EP CAN reject. In practice, it rarely ever DOES.
How the democratic process actually works is important. Public outcry often happens after something becomes LOCAL law (i.e. a few years or months down the road) implemented in a member state. The usual defense from EU-enthusiasts is then “you should have engaged in public debate, it’s too late now”. That should tell you something about the visibility and publicity of the process.
