Ok, but that's a criticism so generic that it's at the verge of being meaningless. By the way, European Commission is technically not elected but it's composed of heads of Member States who are nominated by democratically elected governments - that's a feature, not a bug. And US presidential elections aren't direct either - they are cast through the electoral votes, for reasons. Legislative initiative in EU does not exclusively sit with EC - EP can and does ask for new laws and EC does not have right to reject it at its own discretion. Plus it's not only EP that has this right - there's also direct citizen's legislative initiative where enough signatures gets you EC obliged to consider a draft regulation as if it was raised by EP - https://citizens-initiative.europa.eu/_en

It's all complex but when compared to most nation state laws the EU process is much more transparent and more democratic, although it is much less decisive - there's no presidential decrees etc which is both a limitation at times of war, but also a safeguard against what happened in Russia and is now happening in the US

I very much recommend this book as it goes into great detail on how EU works from inside, dispelling many myths:

https://www.amazon.co.uk/Enraged-Citizens-European-Democratic-Deficits/dp/0857423622