Suppose that you have a basis (contributions for which you did not take a deduction) in your Traditional IRA, and reported these contributions on Form 8606 in the years that you made them (and so the IRS is aware of the basis). In retirement, you are no longer making contributions to the IRA but taking distributions from them. As I understand the matter, the IRS position is that you cannot withdraw the basis first (which is a tax-free withdrawal) and only start taking taxable distributions after the basis has been exhausted; a distribution must be tax-free basis in part and taxable in part where the basis part can be no more than the proportionate amount of the distribution.
(Parenthetical remarks) For the record, in the 1970s, my pension plan had mandatory contributions from post-tax income, and upon retirement, the pension consisted of entirely of the tax-free basis for the first few years, and became taxable income only after the basis had been distributed. In the late 1970s, the contributions were changed to be from pre-tax income and in the early 1980s, the withdrawal rules became like the IRA rules. Thus, by the time I retired a few years ago, my pension plan consisted mostly of pre-tax contributions and tax-deferred earnings on contributions and a small amount of post-tax contributions. Thus, my pension is mostly taxable income and includes only a small amount of tax-free return of the basis.
(Return to main theme) If the basis is $B as of the beginning of 2018, you took a distribution of $D during 2018 and the value of your IRA at the end of 2018 is $R, then (assuming no rollovers or conversions to Roth IRAs etc during 2018), the amount $D x (B/(B+R)) (on Line 12 of Form 8606) is how much is the nontaxable part of the distribution and the amount $D - $D x (B/(B+R)) = $D x (R/(B+R)) is the taxable part (Line 15c). Also, your basis for future years is $B - $D x (B/(B+R)), your previous basis $B less what part of the basis was taken out during 2018 and is computed on Line 14 of Form 8606. These numbers are computed on Form 8606 which the OP does not want to fill out. The instructions on Form 8606 tell us that the amount on Line 15c is to be entered on Line 4b of Form 1040. If one chooses not to complete Form 8606 and simply enters $D on Line 4a and Line 4b as well, one ends up paying income tax on what would have been the nontaxable portion of the distribution. The IRS doesn't care. The rules say that no more than $D x (B/(B+R)) of that $D distribution can be claimed as a withdrawal of tax-free basis; one can always claim less including $0. If you choose to not file Form 8606, you are choosing to pay more tax than you might otherwise need to pay, and a grateful nation thanks you for your patriotic generosity.
So what about future years? Well, the basis is unchanged if no Form 8606 was filed in 2018. Can one resume filing Form 8606 for 2019 for later years? And if so, what should be the basis be when the next Form 8606 is filed? The basis is the same as that reported Line 14 on the last 8606 filed.
The IRS instructions for Form 8606 (cited by the OP) state that there is a $50 penalty for not filing a Form 8606 to report a nondeductible contribution to an IRA, but not for failing to file a Form 8606 in retirement years when no contributions have been made but distributions have been taken. It is worth noting that the instructions also state that in order to verify the claims of basis, one must keep copies of Page 1 of Form 1040 as well as of all Forms 8606 as well as Forms 5498 until the basis has been reduced to zero. Note that separate Forms 8606 are required for Inherited IRAs and one's own IRA.