I think you are slightly confused - the "alternative" that you describe is actually what happened in this case (and in all the cases of retracted papers that I've encountered).
A Retraction Notice has been published at a separate publication [1] with its own DOI, and it cites the original paper [2].
The original paper [2] has been updated to indicate that it has been retracted. In the HTML version, there is an orange banner saying "This article has been retracted". In the PDF version [3] there is a red header, and the retraction notice has been appended as an extra page.
But you are correct that it is important to be able to update PDFs if a significant mistake (or deliberate fraud) is identified.
[1]: https://www.science.org/doi/10.1126/scisignal.abn0168
[2]: https://www.science.org/doi/10.1126/scisignal.aag1064
[3]: https://www.science.org/doi/epdf/10.1126/scisignal.aag1064