> I have yet to understand how an emissions trading system is superior to a simple tax paid on all emissions.

They're more similar than you seem to think. Both internalize cost to the production of pollution. In a tax, the cost is fixed and the total amount of pollution is market-determined. With a cap it is the reverse. However, at the point where the prices agree, they are, in principle, equivalent.

> Trading schemes add a lot of unnecessary complexity and potential for abuse, and enshrine the idea that if you have polluted more in the past, you deserve to keep polluting more in the future.

Allocating pollution licenses to past polluters is only one possible way of distributing them. A cap-and-trade system could also to hold yearly auctions for each year's permits. The former is used many times in part because incumbents are less likely to oppose regulation. They may even be able to achieve efficiencies and sell their allocated permits at a profit because of cap-and-trade. But note that even though the incumbents are receiving the permits for free, they still have an incentive to reduce pollution when the cost of the efficiency is less than the cost of the permit.

> Instead just quantify the total harm caused by emissions the best you can, divide by total emissions amounts, and levy that as a tax per pound of emission.

Two problems is that the harm may be difficult to quantify in a price and more importantly the harm may not be linear in the amount of pollution. You could argue that the optimal solution would be for the government to estimate the harm as a function of the amount of pollution and hold some sort of complicated auction where the price depended on the quantity of pollution permits sold. However, I think this is too impractical for any real-world regulation.

"Trading schemes add a lot of unnecessary complexity and potential for abuse..."

I believe that's exactly why they are "preferred" by our political system. Whenever the political body starts to consider laws about pollution, the lobbyists for the polluters go into high-alert to influence the outcome. They don't want a straight tax, because that'll become a simple cost which is difficult to avoid. Instead they prefer a complex scheme that can be sold as if it has the same impact as the straight tax, but in reality it will provide ways to game the system to either avoid the costs or even make a profit for the polluting companies.