It seems your mind is already made up, given by this statement:

But this is clearly not true.

Your analysis ignores several details.

Commission fees to the broker.

For many brokerages the commissions are zero. You only pay the management fee of the fund, which is typically less than 1% per year.

Capital tax

Taxes on gains can be avoided by either using a tax favored account or by not redeeming your gains each year. Using this method allows the tax that one should pay to compound. Essentially you are taking an interest free loan from the government to invest allowing the "miracle" of compounding interest work for you with even more money. Sure taxes will eventually be due (Exception: ROTH), but you don't have the ability to delay taxes on wages earned.

Inflation & Pay the index fund.

As GOATNine pointed out, the 7% includes inflation. The return of the FIDELITY 500 INDEX over the last 10 years is 9.46%, the fee is a paltry .035%, and the inflation about 2.4% per year. You are looking at a 7.025% return.

Most people do not experience inflation in line with the changes in the CPI.

The tone of your question suggests that you are seeking savings account regular returns but with equity rates. The market just does not work like that. One works, invests regularly, and after a period ends up with a huge pile of money that they did not do much to earn. It is not a get rich quick scheme nor can one pin down a date certain for financial independence.

The market gives, takes away, and then gives again. Studying the chart of the period of 2015 to the first quarter of 2016 is useful. During that time the S&P500 lost money. However, disciplined investors kept investing. It is a good thing too, they were amply rewarded on great run until Jan of 2018.

It seems your mind is already made up, given by this statement:

But this is clearly not true.

Your analysis ignores several details.

Commission fees to the broker.

For many brokerages the commissions are zero. You only pay the management fee of the fund, which is typically less than 1% per year.

Capital tax

Taxes on gains can be avoided by either using a tax favored account or by not redeeming your gains each year. Using this method allows the tax that one should pay to compound. Essentially you are taking an interest free loan from the government to invest allowing the "miracle" of compounding interest work for you with even more money. Sure taxes will eventually be due (Exception: Roth), but you don't have the ability to delay taxes on wages earned.

Inflation & Pay the index fund.

As GOATNine pointed out, the 7% includes inflation. The return of the FIDELITY 500 INDEX over the last 10 years is 9.46%, the fee is a paltry .035%, and the inflation about 2.4% per year. You are looking at a 7.025% return.

Most people do not experience inflation in line with the changes in the CPI.

The tone of your question suggests that you are seeking savings account regular returns but with equity rates. The market just does not work like that. One works, invests regularly, and after a period ends up with a huge pile of money that they did not do much to earn. It is not a get rich quick scheme nor can one pin down a date certain for financial independence.

The market gives, takes away, and then gives again. Studying the chart of the period of 2015 to the first quarter of 2016 is useful. During that time the S&P500 lost money. However, disciplined investors kept investing. It is a good thing too, they were amply rewarded on great run until Jan of 2018.