"All that the corporation tax adds to this picture is the creation of work in tax avoidance services, and an unjust inequality between those firms that can afford those services and are structured to take advantage of the rules, and those that can not and are not."
This already exists in the United States.
An "S-Corp" is a passthrough corporate entity wherein the corporation (or partnership) is not taxed at all and all profits flow to the owners of the entity who are then bound to pay the taxes on their personal returns.
Almost all small businesses incorporated in the US are such entities. It is not exotic in any way and is totally accepted and normal.
The trick is ...
With some minor exceptions, all of the profits need to flush out of these passthrough entities every year. You can't just keep piling up untaxed profits in the company bank account. The corporation is required to disburse the profits and create taxable income for the owners.
Big coporations which are not passthrough entities can keep the money and do not have to disburse it ... but they have to pay taxes on it.
So there are pros and cons to these structures.
I personally feel that passthrough corporate entities are much simpler, much more comprehensible and do not have the societal inefficiencies (pursuing tax avoidance strategies, for instance) that you mention. But at the same time I think we're asking for trouble if we let (big multinationals) just pile up bigger and bigger mountains of cash in their bank accounts, untaxed.
So, in absence of a better solution, taxing non-passthrough entities seems like the least worse solution ...