You can absolutely do your own taxes, either on paper and mail the forms or (possibly) via the Free File Fillable forms mentioned on the page you linked (as long as you don't hit a corner case). The Free File Fillable forms page [0] says "Make sure we fully support the forms you need" and links to another page with a lengthy list of limitations [1].
So yeah, we're in a place where the IRS says taxpayers "should file electronically with direct deposit if at all possible" [2] but also informs taxpayers that not everyone can use the IRS's forms to file electronically.
0: https://www.irs.gov/e-file-providers/free-file-fillable-form...
1: https://www.irs.gov/e-file-providers/free-file-fillable-form...
2: https://www.irs.gov/newsroom/irs-begins-2022-tax-season-urge...