I can't for the life of me understand how people get the misconception that this one factoid equates to a tax rate equivalent in some magical vague way.
1. If it closed any loopholes it only did so to open more convenient ones we are currently still struggling with that go to wealthy individuals and companies far more than the middle class, which most of those loopholes you are taking about were for prior to reagan. They were less loopholes and more accurately social safety nets put in place after the great depression.
2. The "effective" tax rate is a more or less meaningless number contrived to hide the nature of what is actually occuring. It's a way of obviscating the raw revenue but you can very easily cut through it by simply counting the currency in circulation and determining how much of it is in the hands of the wealthy vs regular people. When you do that you find that raw inequality is on par with what it was on the eve of the great depression and there are plenty of papers to support that this is no coincidence.
Secondly you conveniently lock the rate at regan without pointing out that immediately prior to regan there were significant changes in taxation. In the 50s for example it wasn't uncommon to tax a CEO and their company at 90%, which is widely different than the tax rates we see now even if we use the arbitrarily designed "effective" qualifier.
3. This makes assumptions that the tax rate reflects actual taxation which it doesn't. You are correct that if you look at the books quickly the effective tax rate seems on the level but look even a bit more closely and things quickly don't add up.
Many companies corporations and individuals pay nothing yearly in taxes by using the location of their business to avoid having to be taxes in one country vs another or one state/province over another. They flood vast sums of money to shell companies and then report themselves as only having earned 300,000 (as bezos has done for the last 5 years) in order to present this falsehood that he doesn't take the money, but instead he gets paid in stock which can be far more flexible with taxation and isn't accounted for in your "effective tax rate"