This isn’t true, they are the only body that can draft legislation, but the Council and Parliament can propose legislation for them to draft (though they have refused to do so on at least one occasion), EU citizens can also propose legislation.
Moreover, unlike almost any civil servant elsewhere in the world, whilst their legislative proposals are subject to the approval of MEPs and nation states, their actions in running the executive are not. They are specifically not accountable to MEPs, who’s only sanction is to sack the whole lot en masse. Unsurprisingly, this is not often used.
This is definitely one of the areas that could be improved.
The commission was created as an independent body to regulate the work the of the two main branches of the EU, I think it’s important that it retains its independence, but that doesn’t mean it should be totally immune from all outside influence, need to be careful not to swing too far the other way though.
To take a US example, it’s like the President being appointed, not elected, and able to decide which laws congress and the senate make.
It would more be like the President being elected by Congress, which is what happens in many countries.