It says nothing about why it's a problem that people with high incomes also get this (other than it's unfair).

That's a pretty good reason. It's using the income of taxpayers to subsidize seniors with above average income. Yes, about half of that is clawed back, but it's a poor use of resources.

It then suggests making it more complicated (increasing overhead) so that poor people can get more.

Payouts are already scaled by income. Changing the scaling rates does not increase complexity, but it does improve fairness.