You’re right about that main point, and I definitely agree with that point. I think the main advantage of Roth is the tax free growth. In your calculation, you only consider federal income tax. If you plan to retire in a no income tax state, then great, but I plan to retire right here in SD, so I’d have to add about 10% on top of that.
You’re right regarding the progressive tax code. I totally forgot about that. It does bring the federal tax rate down from the 25% I was using to calculate. So, let me try this again. Assuming someone is 30, and start saving for retirement now and put $15k/yr away. Lets assume this individual stay w/in the 25% fed tax rate (to make things simpler). This person will retire at age 60. Over 30 years, this person put away $450k into their 401k. Lets assume there’s no major gap in employment and the investment grow at 8% over 30 years. With Roth, you’re paying $112k in federal tax. With traditional, that $450k should grow to $1,879,213.91. Lets assume you’re splitting that $1.8M up over time so you’ll stay w/in the 25% tax bracket, so the effective tax rate due to the progressive tax code will be 15% as you mentioned. 15% of the $1.8M is $281882. So, you’re still going to pay roughly $170k more in taxes.
The other big advantage of Roth vs traditional is required minimum distributions. Roth does not have that until you die, while traditional require you to take $ out at age 70.5. It really depends on how big is your nest egg outside of your retirement account. If you did a good job in saving for retirement beyond your 401k/IRA, having a Roth means you don’t have to take $ out and raise your tax bracket when you don’t really need to. People in the middle of the 25% tax bracket, should be able to save about $1k-3k/month beyond maxing 401k/IRA. If that person invest and get 8% return over 30 years, they should have a nest egg of $1.5M-$4.5M in taxable account.
The big unknown is inflation. If inflation go wild or just run faster than it has been for the next 30 years, 8% return would be too small. If we have average deflation over the next 30 years, 8% would be too large. If one bet on inflation, Roth seems even more lucrative while if one bet on deflation between now and retirement, traditional would be a better vehicle. Assuming the deflation will cause your average return to be less than 1.7% over 30 years vs 8%.