However the real problem is political capital, if parliament wanted to they could just refuse to adopt any law or budget etc unless X member of the commission resigns or Y bill is proposed by the commission. The power is there, and this is essentially how parliaments evolved over history, wrestling power away from the monarchs (or in this case they'd be wrestling power from the heads of government in the European Concil)

But because the EP lacks visibility and people are generally uneducated in how the EU works the MEPs won't take the risk even if they felt it was needed and they will hardly be punished for not taking it because people vote MEPs in based on national politics and not their positions in the EU

There aren't really more powers to be given to the parliament, you could make censure of the commission being 50%+1 instead of 2/3 and letting them officially initiate legislation, but those are minor changes and won't change the underlying awareness problem

Even in this thread on a platform on which you'd expect people to be reasonably educated and capable of googling before commenting half of the comments about what the EU and institutions can do are completely uninformed

Even the article in the submission is attacking the European Commission by discussing claims made by an organization entirely distinct from the EU

(The EC draft is deserving of many attacks but it has enough wrong in it not to require bringing in something entirely unrelated)