It is usually better to put after-tax money in a Roth IRA over putting it into a regular account or in a Traditional IRA, or, if you cannot put the after-tax money directly into a Roth, put it into a traditional IRA and then quickly convert it to a Roth (a "back-door" Roth).
The rest of this answer assumes that you put after-tax money into a traditional IRA and don't convert it to a Roth.
One way to think about your question is to put it this way: is it better to put after-tax money in (1) a traditional IRA, or (2) in a regular (non tax-advantaged) account?
Keep in mind that contributing after-tax money to a traditional IRA (or to a 401(k)) has the advantage that the earnings grow in a tax-deferred environment, but you will eventually have to pay taxes on the earnings you withdraw.
So, which is better? The answer: it's complicated.
Two important factors that affect the answer:
The difference between your pre-retirement and retirement tax rates (don't forget to take into account both federal and non-federal income taxes).
The tax rate on your earnings.
Simplifying assumptions: You have P dollars to invest. You invest in a fund that pays a constant Q return each year. You don't touch the money until you withdraw it all at the end of N years. For the non tax-deferred account all earnings would be taxed at a rate of S and are paid for by withdrawing from the account. Your retirement tax rate is R. We assume that the qualified earnings rate is 15%. All contributions to the tax-deferred account are after-tax. Finally, we assume that you don't convert the traditional IRA into a Roth.
Scenario 1. You invest the money in a regular (non tax-advantaged account). After N years the balance would be P(1+Q-QS)^N.
Scenario 2. You invest the money in a traditional IRA (or 401(k)). After N years after withdrawing (and paying the taxes) the balance would be P((1+Q)^N(1-R)+R).
Example 1. [Qualified earnings] All earnings are "qualified", so S=0.15. Assume further that Q=0.05 and R=0.24. After 10 years the return on the non-IRA is 51% while the return on the IRA is 48%.
Example 2. [Non-qualified earnings, low tax-rate] Your pre-retirement tax rate is 24% and none of the earnings are qualified, so S=0.24. Assume further that Q=0.05 and that R=0.24. After 10 years the return on the non-IRA is 45% while the return on the IRA is 48%.
Example 3. [Non-qualified earnings, high tax-rate] Your pre-retirement tax rate is 32% and none of the earnings are qualified, so S=0.32. Assume further that Q=0.05 and that R=0.22. After 10 years the return on the non-IRA is 40% while the return on the IRA is 49%.
Summary: if you cannot get a qualified rate on your earnings and your retirement tax rate is substantially lower than your pre-retirement rate it makes sense to put after-tax money in a tax-deferred account, otherwise probably not. But to be sure you have to do the math (and your guesses about your retirement tax rate have to be correct).