Money money money(and life...)
So why is it so difficult to ban artificial fertilizers? The simple answer to that is population. The more complex answer is population and economics. Currently the human population is heavily sustained by the use of artificial fertilizers, in fact it is estimated that 40-60% of the current crop yields are due to artificial fertilizers and that is expected to increase. That means that a large portion of the human population is sustained via the use of these additives. From this it can be seen that without some replacement, or a massive depopulation(unlikely and unethical) artificial fertilizers are here to stay.
As for replacement, there aren't many options that are feasible. Artificial fertilizers rely heavily on fossil fuels in their production in the form of natural gas (which is non-renewable, but that's yet another issue to be dealt with), and there aren't many other substances that can offer that level of potential energy. Manure based fertilizers, such as chicken litter are sold at a premium for several reasons, not the least of which is that it's more effective, but also because it's more rare. There is a similar situation with other forms of manure.
This gets even more tricky when the issue is brought to light that organic fertilizer doesn't solve the problem. In some senses, even "organic" fertilizer is still artificial...it is still trucked in, it is still added to the dirt, it is still an artificial runoff. It is also effective and has some unusual properties, most notably controlled release, which makes it more desirable than synthetic fertilizer for certain applications. However it will still runoff into waterways where it will facilitate the growth of plants, leading to dead zones. Any additive to the earth that can run off will face this problem which is why the situation gets so complicated.
The primary solution proposed for this is to control runoff. This is, however, expensive...and corporations that control the food supply dislike seeing cuts in their profits. Without a clear economic incentive to control waste water runoff it is unlikely to be possible to reduce the outflow into the rivers, and therefore control the algal growth.