A 2009 feature request to add support for Markdown footnotes was declined in 2014.
The reason(s) for declining appear to no longer be valid:
We want to avoid creating proprietary additions to Markdown
Stack Exchange already supports additions to the CommonMark specification, such as tags, spoilers, syntax highlighting for code, and tables. See, for example, the announcement of table support from 2020, which explicitly acknowledges this and says that the GitHub-flavored markdown table extension is "stable and usable enough to serve our purpose".
Since the CommonMark specification has already been extended and GitHub-flavored Markdown is already in use, it no longer seems valid to claim that there is a desire to avoid proprietary extensions or additions to the CommonMark specification. The use of the GitHub-flavor extension for footnotes is no different than the use of GitHub-flavor extension for tables.
We do not have consensus that footnotes are something to be encouraged
We can check based on the voting of this question, but the original feature request question and the vast majority of the answers have a net-positive score today. Only two answers claim that the feature is unnecessary - the accepted answer (which also outlines a workaround) and one answer scored at -2.
A work-around exists (albeit an ugly one)
The workarounds are only partial. Although you can use HTML tags to create superscript text, the workarounds and comments on them point out issues with user experience, readability, and navigability. In addition to human readability improvements (in both the Markdown editor and the rendered output), this also opens the possibility to mark the content for machine readability and denoting content.
Implementing this feature can assist with better ways to reference material written by others, such as some sites encouraging or requiring more formal citations of content that are difficult to do in-line. Across the network, it can give authors a better way to put supporting or clarifying content without interrupting the flow of the key points of the answer.
<a hreaf="#note1-footnote"to jump down to the footnote,<a hreaf="#note1-source"(with appropriate IDs applied on the source/footnote elements) to jump back. The browser then handles the jump to the named elements. Yes, a markdown consumer needs to be changed to generate this. But that's going to be the case whatever you really want to do - nobody is "withholding" markdown features. They just need to be added.