Why? Again, it has to do with ability. You don't approve driver's test system on a referendum, right? You don't approve doctors' licensing system on a referendum. It just has to be public that's all.
Right, and I just described what changes I would like to see in it. Moreover, we could also skip the presidency at all. All major policies should be determined by direct voting of able citizens (thus, skipping the necessity of parliament at least). We now have the technology for direct democracy (without representatives).