Should 1040-X be filed on changes that have no impact?

If the change in income on the 1099 is so small that the tax owed doesn’t change, I wouldn’t bother.

However, If we are talking about a 1099-NEC for your business, I just want to point out that you are supposed to report all income, whether or not it appears on a 1099-NEC. Ideally, you keep your own records, and then your return doesn’t change even if there is a mistake on a 1099 or a corrected one appears later. This is different than an incorrect W-2, where you really do need to be sure that the amounts on it are correct.

You might need to file it anyway--the problem is matching. If they have you claiming $10000 in income but a modified 1099 for $10001 the computer is going to think that's $10001 in unreported income.

A frivolous return, roughly, is one that is so unresponsive, erroneous, or ridiculous that it can be presumed to be in bad faith. Sincerely correcting an error, even a minor one, is not frivolous.

You do not need to file the updated 1040 itself with the IRS (the 1040-X serves to convey that information).

A suggestion would be to complete a pro-forma 1040 or 1040-X with the corrected income and document for your records that there will be no change in the tax owed. Don't consider anything frivolous, but keep it on hand in case its needed. Be aware that at some point the IRS may electronically audit your return by checking your 1099 investment-account reported income against the 1099 income reported to the IRS by your broker or investment/wealth manager, and/or from other reporting sources. If the difference is deemed significant, the IRS will send you a letter of inquiry regarding the difference in income and the amount of tax owed. In that case, you will need to file a 1040-X and pay the tax. This is typically done with a brief cover letter from you explaining the error, and what was done in correction, along with attachment of the 1040-X and means of payment. Be aware such inquiry letters from the IRS can result in a refund if filing the 1040-X shows the error was in your favor and that you incurred a refund rather than tax owed. You can generally determine the best path to handle these issues, but if there are still questions, sound advise would be the ask a tax professional or directly talk to someone at the IRS.

Regarding the 1040-X and a corrected 1040, you do not need to also file a corrected 1040. You just file the 1040-X. As you walk your way through the 1040-X, you will see that all of the changes you would have made to your 1040 will be documented line-by-line on the 1040-X. You will have to attach any revised schedules if they are required. If you are using purchased tax software, you will find that you can go through filling out the 1040-X by directly inputting everything line-by-line directly on the 1040-X working form. Otherwise you can choose to let the software lead you through the process of making the changes as though you were doing a revised 1040, and thereby get the same 1040-X result. You need to verify the math is correct - check the additions and subtractions and verify the numbers. Tax software generally has very well documented help dialog boxes with references to IRS pubs and info. But should you still have questions or want more direct answers, talk to a tax professional or someone at the IRS.