Tax-advantaged accounts mean you pay less tax. You fundamentally pay less tax on IRAs and 401ks than other accounts. That's their benefit. You keep more money at the expense of the government. It makes sense for the government to limit it.
If you don't understand why you pay less tax, you must consider the time value of money -- the principal now is the same value of money as the principal + earnings later.
With IRAs and 401ks, you only pay income tax once: with Roth IRAs and 401ks, you pay tax on the entire amount of money once when you earn it; with pre-tax Traditional IRAs and 401ks, you pay tax on the entire amount of money once when withdraw it.
However, with outside accounts, you have to pay tax more than once: you pay once when you earn it, and pay tax again on the earnings later, earnings that grew from money that was already taxed (which, when considering time value, means that the earnings have already been taxed), but is taxed again. For things like savings in a bank, it's even worse: interest (which grew from money already taxed) is taxed every year, which means some money you pay tax on n times, if you have it in there n years.
If you don't understand the above, you can see with an example. We start with $1000 pre-tax wages and for simplicity will assume a flat 25% income tax rate, and a growth rate of 10% per year, and get the cash (assume it's a qualified withdrawal) in 10 years.
- Pre-tax Traditional IRA or 401k: Start with $1000. After 10 years, it grows to $1000 * (1.1)^10 ~ $2593.74. After 25% tax, we have $2593.74 * 0.75 = $1945.31.
- Roth IRA or 401k: Start with $1000. After 25% tax, we have $750. After 10 years, it grows to $750 * (1.1)^10 ~ $1945.31. Note that this is the same as the Traditional IRA. This is because in both cases, we pay tax on the same time value of money -- the principal at the time of contributing is equivalent to the principal + earnings at the time of withdrawal.
- Savings account, short-term capital gains, or other income which is taxed each year: Start with $1000. After 25% tax, we have $750. Each year, we earn 10%, but pay tax on 25% of that, so we actually earn 7.5%. After 10 years, it grows to $750 * (1.075)^10 ~ $1545.77.
- Long term capital gains:
- if taxed at the same rate as regular income: Start with $1000. After 25% tax, we have $750. After 10 years, it grows to $750 * (1.1)^10 ~ $1945.31. Then the $1195.31 in earnings will be taxed again to leave $1195.31 * 0.75 = $896.48, for a total of $1646.48.
- if taxed at the 15%: Start with $1000. After 25% tax, we have $750. After 10 years, it grows to $750 * (1.1)^10 ~ $1945.31. Then the $1195.31 in earnings will be taxed again to leave $1195.31 * 0.85 = $1016.01, for a total of $1766.01.
- Capital gains would have to be taxed at 0% to match the advantage of IRAs/401ks.