If the EU is fundamentally broken because the head of the Commission isn’t a direct vote, then so are the US, Austria, the UK, Germany, Canada, …
Even then, all the power is in the Commission; the Commission is split in areas (competition, energy, trade, etc.), and each country nominates a commissioner in each area, and the total Commission gets approved once again by democratically elected Parliament. The head of the Commission has only one single vote, and a majority vote decides if anything passes, and even the Parliament has to approve it. That said, I think we all want Parliament to have the ability to propose legislation.
So don't take this ignorant take in here and present it as some kind of dictatorship and a fundamental flaw of the EU that undermines it all; the EU has been a massive positive force for the continent, and people like you just like to shit on it.
Even the Americans don't elect their president directly, they have a special council inbetween to distribute more power to the sparsely populated states.
Russia is a direct democracy (the people do directly elect their leader) but also the example of why technicalities like that make no difference in how fair politics are.
The representatives from the parties are free to choose whoever they want, but generally it becomes a leader of the largest party in the governing party/coalition.