Legitimacy maybe, but democratic legitimacy is absolutely lacking. A country governed the way the EU is, would not be considered sufficiently democratic. The democracy for the commission is very indirect.

People vote for their national parliament. Parliament appoints a government. Those appointed governments then discuss who to appoint in the commission. Europarliament gets a say, but can only accept or reject the entire commission, not specific members in it.

The Europarliament is the only democratically elected body on the EU level, and its power is sorely lacking.