"Can, may, and should, are all treated differently. The taxpayer can pretty much do anything they want to, even if it is subject to penalty and/or excise tax and/or income taxes."

Sir, what I stated in my previous reply and sources I provided is how 2021 and 2022 ineligible Roth contributions must be treated and reported according to the guidance in order to stop the 6% penalty from keep accruing each year on excess, and if you want to treat and to report it correctly. No one is saying anything about may or can. The only choice the taxpayer is explained and is considering is to whether they want to leave the 2021 earnings in the Roth IRA or withdraw it. You don't continue accruing 6% penalties on the earnings if you leave only the earnings in the account, because by removing the original contribution, you are removing the excess. If the taxpayer wants to withdraw the earnings associated with the excess contribution as well now or later, then it simply will be treated as an early or normal withdrawal depending on the age. That is it. The earnings do not continue incurring a 6% penalty each year if they remain in the account, or if they are withdrawn later. So I let the taxpayer decide what she wants to do with the 2021 earnings since there is no penalty or tax for letting it stay in the account. Whether she withdraws the 2021 earnings or not, she still has to pay the 6% penalty on the actual excess contribution amount for 2021 and for 2022 either way ( 6k actual contribution in this case) but not on the earnings.

"I thought I already mentioned that there is a recommended strategy to leave Roth earnings year-over-year, knowing full well it incurs tax and/or penalty, because the person making the recommendations thinks you will easily beat the 6% penalty in the earnings."

You will not incur 6% tax or penalty on the earnings by leaving Roth earnings with the untimely correction. And no one is making the recommendations you suggested. The taxpayer discovered this year that she made excess Roth contributions for 2 years, and now we need to resolve this. That is it. The point of my previous reply was to point out that you and I were wrong about the earnings. You kept saying that the 2021 earnings must be withdrawn and or they will be taxable and or need to be reported, since you believe that you are not allowed to have tax free earnings from ineligible contributions. I thought that too originally. But this was incorrect. The IRS does not require calculation of earnings with the untimely correction. And you do not need to withdraw the earnings with the untimely correction. You can leave the earnings and it is allowed to compound tax free. You only need to remove the contribution to stop the 6% penalty, not the earnings. And you will not be paying the 6% penalty on the earnings. You would continue paying a 6% penalty for each year IF you do not remove the original excess contribution. Leaving earnings in the account does not create a 6% penalty on the earnings. By making a distribution of your original contribution, you are eliminating the excess contribution. That is it. 

As per Tax Adviser : .."The taxpayer then makes an ordinary distribution of $7,000 that is composed entirely of nontaxable investment and that eliminates the $7,000 excess contribution. The $700 of earnings is retained by the Roth IRA and is allowed to compound tax-free in future years.”

https://www.thetaxadviser.com/issues/2020/apr/correcting-excess-contributions-iras.html

Tax Adviser always posts very comprehensive, detailed, accurate, information citing the IRS codes as well and with examples. The Fidelity link I posted above also clarifies that.

And here is another source if that's easier to understand. It says:

"If you remove the excess contribution AFTER the tax deadline, you do not have to pay taxes or penalties on the EARNINGS portion because you are not required to distribute the earnings, but you pay a flat 6% penalty per year based on the actual excess contribution amount.

Example:  You contributed $6,000 to your Roth IRA in 2022, your income ended up being too high to allow any Roth IRA contributions in 2022, you discover this error in November 2023.  You will have to withdraw the $6,000 excess contribution, pay the 6% penalty of $360, but you do not have to distribute any of the earnings associated with the excess contribution.

Why does it work this way?  This is only a guess, but since most taxpayers probably try to remove the excess contributions as soon as possible, maybe the 6% IRS penalty represents an assumed wipeout of a modest rate of return generated by those excess contributions while they were in the IRA."

https://www.greenbushfinancial.com/all-blogs/roth-ira-excess-contributions

"I would point out if that is true, why not just make that a regular investment?"

This post is about to handle excess Roth IRA contribution for previous years, sir. Not to ponder the investment options. The taxpayer had no intention to make excess Roth contributions, but did so for 2 years due to the incorrect information given to her by someone else. Now, she asked me for assistance to prepare 2022 returns, and I discovered that her Roth IRA contributions were 100% excess, so we are trying to resolve the issue. Her former tax preparer who prepared her 2021 returns failed to bring it to her attention. The recharacterization of 2021 to a traditional IRA is not an option either because it is too late. Recharacterization of 2022 Roth IRA to traditional is possible, but it makes no sense to do since she can just withdraw it before the 2022 tax return due date thus treating it as the contribution never happened. And she can just open a traditional IRA after if she wants. I already advised the taxpayer of her IRA options with her income. Not relevant to this issue here. This issue took a lot of time, research, etc to figure out, but I have it all figured out now and how to report it on tax returns as well. Instructions on forms 5329 and 8606 make a lot of things very clear as well. 

On another note, that is exactly why this "strategy" has been used lately. This is not my client's situation, but a strategy that has been gaining some popularity as of late surrounds the concept of making excess contributions to a Roth IRA in order to generate additional tax-free returns in the Roth IRA. Since the 6% excise tax only applies to the amount of the Roth IRA excess contribution and no 10% penalty or income tax would apply to the amount of the excess contribution, in addition to the earnings on the excess contribution remaining in the Roth IRA and able to grow tax-free, the idea is that the 6% excise tax on the excess Roth IRA contribution will end up being considerably less than if the investment was made with personal funds subject to the individual income tax rates.

Hence, the excess Roth IRA contribution strategy is based on the notion that paying a 6% tax on excess contributions to a Roth IRA, while gaining the tax advantage of having the earnings from the excess contribution remain in the Roth IRA so it can grow tax-free, is a great deal compared to making the same investment with personal funds and having to pay income tax on the earnings and gains.