> The Parliament acts as a co-legislator with equal legislative power in this process

I think that's misleading. Correct me if I'm wrong, but as I understand it, only the Council can propose legislation, while the Parliament can only accept or reject the Council's proposals [1]. Meaning that the Parliament can neither change nor reverse course - it is completely decided by the Council. All the Parliament can do is limit how fast that course is followed.

Edit: Sorry, what I wrote about the "Council" should have been about the "EU Commission" instead. The Council may in fact have equal power, as you wrote.

[1] Which I think (but was unable to explicitly confirm) extends to removing old legislation. I.e. the Council only has to get its way once, and then we're stuck with a law, unless the Council proposes to remove it. A ratchet.