I think something that would help to make people much more aware of their tax rates is getting rid of automated W-2 deductions, so that virtually all taxpayers would individually have to pay money out of their own bank accounts.
Having the filing process be complicated or tedious doesn't really do much to give people a more accurate perspective on the financial burden of taxation to them. If you could get your tax forms filled out automatically in 10 seconds but the result was "you have to send the IRS a check for $10,000", that would have a far greater awareness-building effect than having to spend 4-6 hours dealing with forms and paperwork only to conclude that "you don't owe any taxes" (because the money was already withheld as you earned it over the course of the year).
Of course, this change would also cause a lot of hardship because quite a lot of people would find it difficult, for various reasons, to save up money to pay taxes if they weren't having someone else do it for them automatically. And I'd expect that this hardship would probably lead more in the direction of political pressure to reinstitute W-2 deductions rather than pressure to reduce or eliminate income taxes.
Having worked on W-2 (salary with automatic deduction from each paycheck) for my whole life until last year, when I switched to 1099 (making quarterly estimated tax payments and sending the tax authorities a check), I really had the "wow, I never quite noticed how much I was paying in taxes before!" experience.