I don't think this is true, but aside from that, what would you do instead?
I love the idea of simplifying the tax code, but I think if you're arguing it's useless to tax the rich I think you have to think that would be useless too, right? We'd need to actually have the rich pay their rate, but you're saying that doesn't work.
[0]: https://www.heritage.org/budget-and-spending/report/50-examp...
Every deduction exists because someone wants it to exist. And “eliminate all deductions” lasts until someone goes “but what about the child credit” or any other issue.
This will continue as long as Americans continue to be averse to the idea of actual cash transfers and continue to use the tax code as a backdoor system for remitting subsidies and credits.