So this is typical of criticism of the EU democratic structure: It's just factually wrong. The EU Parliament can dismiss the commission. From Wikipedia:
"The Parliament also has the power to censure the Commission by a two-thirds majority which will force the resignation of the entire Commission from office. As with approval, this power has never been explicitly used, but when faced with such a vote, the Santer Commission then resigned of their own accord."
The fact that the whole democratic setup is highly complex is in itself a problem. But the concrete deficits people mention are never true or don't apply to other democracies either...
In practice the EU Parliament has been a lot more trouble for the executive than is typical in national bodies. The one valid point is that the parliament does not have the right to initiate legislation itself. That is unusual, but in practice many people who are actually close to political processes seem to say this is mostly symbolic, as national bodies can't really draft effective legislation without cooperation from the executive either... Stil definitely something I would love to see addressed.