The concept of “tax burden” or more precisely “tax incidence” is a rather complex topic. For instance, no consumer pays gas taxes since the gas station pays them all, but most people are smart enough to realize the consumer bears a lot of the burden of fuel taxes even though none pays it directly. There is the question of who faces the burden of corporate taxes? Executives? Stock holders? Employees? Consumers? This question has been studied extensively, and with so many multinational companies, in the long term employees are the most burdened by the tax because corporations make investments in lower tax areas. The cost of an investment in a location are wages+taxes. If taxes are high, then wages must be lower for the investment to make sense. This only becomes true in the long term, but it is a good argument for lower corporate taxes and higher capital gains taxes.

The argument is that dragging on corporations hurts customers and staff as well as owners. It's better to precisely target the owners.

However, I think it misses that most of the benefit to owners is in the form of unrealized gains, not subject to any of the tax rates that people talk about tweaking.

No, corporate tax is of corporate profits, which is just capital gains that haven't been dispersed and may be dispersed in the future (or may be reinvested). Salaries and wages are not profits, so they are not subject to the corporate tax. In theory, the sum of the capital gains rate + corporate tax rate is supposed to approximate the individual income tax rate.

But because most people will never understand this, we can't have a tax code that makes sense. Mass democracy is incompatible with sensible rulemaking in this area.

To improve society.